Triangles Row Sum Power3

Powers of 3

A013609 Triangle of coefficients in expansion of (1+2*x)^n.

A038207 Triangle whose (i,j)-th entry is binomial(i,j)*2^(i-j).

A038622 Triangular array that counts rooted polyominoes.

A065109 Triangle T(n,k) of coefficients relating to Bezier curve continuity.

A067337 Triangle where T(n,k)=2*T(n,k-1)+C(n-1,k)-C(n-1,k-1) and n>=k>=0.

A102756 Triangle T(n,k), 0<=k<=n, read by rows defined by: T(n,k) = T(n-1,k-1) + 2*T(n-1,k) + T(n-2,k-2) - T(n-2,k), T(0,0) = 1, T(n,k) = 0 if k < 0 or if n < k.

A103286 Triangle, read by rows, where row n+1 is formed by sorting, in ascending order, the result of the convolution of row n with {2,1}.

A104029 Triangle, read by rows, of pairwise sums of trinomial coefficients (A027907).

A105728 Triangle read by rows: T(n,1)=1, T(n,n)=n and for 1<k<n: T(n,k)=T(n-1,k-1)+2*T(n-1,k).

A114283 Sequence array for binomial transform of Jacobsthal numbers A001045(n+1).

A120058 Coefficients for obtaining A120057 from Bell numbers.

A120909 Triangle read by rows: T(n,k) is the number of ternary words of length n having k runs (i.e. subwords of maximal length) of identical letters (1<=k<=n).

A120910 Triangle read by rows: T(n,k) is the number of ternary words of length n having k levels (n>=1, 0<=k<=n-1). A level is a pair of identical consecutive letters).

A120987 Triangle read by rows: T(n,k) is the number of ternary words of length n with k strictly increasing runs (0 <= k <= n; for example, the ternary word 2|01|12|02|1|1|012|2 has 8 strictly increasing runs).

A124730 Triangle, row sums = powers of 3.

A124731 Triangle, row sums = powers of 3, companion to A124730.

A125076 Triangle with trigonometric properties,

A125170 Binomial transform of an infinite lower triangular matrix with (1,1,2,4,8...) in every column and the rest zeros. Let the left column = A007051, then for k>1, T(n,k) = (n-1,k) + (n-1,k-1).

A125185 Triangle read by rows: T(n,k) is the coefficient of t^k in the polynomial S(n,t)=[(1+t)(2+t)^n+(1-t)t^n]/2 (0<=k<=n).

A126136 Binomial transform of A107430.

A131048 (1/3) * ((A007318^2 - A007318^(-1)).

A135233 A007318 * A193554.

A140169 Triangle read by rows, iterates of X * [1,0,0,0,...] where X = an infinite bidiagonal matrix with (2,1,2,1,2,1,...) in the main diagonal, (1,2,1,2,1,2,...) in the subdiagonal and the rest zeros.

A153279 Eigentriangle by rows, T(n,k) = A000079(n-k) * (diagonalized matrix of (1,1,3,9,27,81,...)).

A164975 Triangle T(n,k) read by rows: T(n,k) = T(n-1,k)+2*T(n-1,k-1)+T(n-2,k)-T(n-2,k-1), T(n,0) = A000045(n),0<=k<=n-1.

A164981 A triangle with Pell numbers in the first column.

A172249 Triangle, read by rows, given by [0,1/3,-1/3,0,0,0,0,0,0,0,...] DELTA [3,-1/3,1/3,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938.

A182436 Triangle T(n,k), read by rows, given by (2, -1, -1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

A183190 Triangle T(n,k), read by rows, given by (1, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (0, 1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

A185081 Triangle T(n,k), read by rows, given by (0, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 1, -1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

A208532 Mirror image of triangle in A125185; unsigned version of A120058.

A208749 Triangle of coefficients of polynomials u(n,x) jointly generated with A208750; see the Formula section.

A208750 Triangle of coefficients of polynomials v(n,x) jointly generated with A208749; see the Formula section.

A208751 Triangle of coefficients of polynomials u(n,x) jointly generated with A208752; see the Formula section.

A208752 Triangle of coefficients of polynomials v(n,x) jointly generated with A208751; see the Formula section.

A208757 Triangle of coefficients of polynomials u(n,x) jointly generated with A208758; see the Formula section.

A208758 Triangle of coefficients of polynomials v(n,x) jointly generated with A208757; see the Formula section.

A208763 Triangle of coefficients of polynomials u(n,x) jointly generated with A208764; see the Formula section.

A208764 Triangle of coefficients of polynomials v(n,x) jointly generated with A208763; see the Formula section.

A209125 Triangle of coefficients of polynomials u(n,x) jointly generated with A164975; see the Formula section.

A209128 Triangle of coefficients of polynomials u(n,x) jointly generated with A209129; see the Formula section.

A209129 Triangle of coefficients of polynomials v(n,x) jointly generated with A209128; see the Formula section.

A209130 Triangle of coefficients of polynomials v(n,x) jointly generated with A102756; see the Formula section.

A209131 Triangle of coefficients of polynomials u(n,x) jointly generated with A209132; see the Formula section.

A209132 Triangle of coefficients of polynomials v(n,x) jointly generated with A209131; see the Formula section.

A209137 Triangle of coefficients of polynomials u(n,x) jointly generated with A209138; see the Formula section.

A209138 Triangle of coefficients of polynomials v(n,x) jointly generated with A209137; see the Formula section.

A209240 Triangular array read by rows. T(n,k) is the number of ternary length-n words in which the longest run of consecutive 0's is exactly k; n>=0, 0<=k<=n.

A210225 Triangle of coefficients of polynomials u(n,x) jointly generated with A210226; see the Formula section.

A210227 Triangle of coefficients of polynomials u(n,x) jointly generated with A210228; see the Formula section.

A210233 Triangle of coefficients of polynomials u(n,x) jointly generated with A210234; see the Formula section.

A210235 Triangle of coefficients of polynomials u(n,x) jointly generated with A210236; see the Formula section.

A210557 Triangle of coefficients of polynomials u(n,x) jointly generated with A210558; see the Formula section.

A210563 Triangle of coefficients of polynomials u(n,x) jointly generated with A210564; see the Formula section.

A210792 Triangle of coefficients of polynomials v(n,x) jointly generated with A210791; see the Formula section.

A210793 Triangle of coefficients of polynomials u(n,x) jointly generated with A210794; see the Formula section.

A210794 Triangle of coefficients of polynomials v(n,x) jointly generated with A210793; see the Formula section.

A247936 Riordan array ((1-2x)/(1-3x), 2x).

A287326 Triangle, T(n,k) = 6*k*(n-k) + 1, row sums = powers of 3.

Even powers of 3 , powers of 9

A013615 Triangle of coefficients in expansion of (1+8x)^n.

A013623 Triangle of coefficients in expansion of (2+7x)^n.

A013628 Triangle of coefficients in expansion of (4+5x)^n.

A038224 Triangle whose (i,j)-th entry is binomial(i,j)*3^(i-j)*6^j.

A038246 Triangle whose (i,j)-th entry is binomial(i,j)*5^(i-j)*4^j.

A038257 Triangle whose (i,j)-th entry is binomial(i,j)*6^(i-j)*3^j.

A038268 Triangle whose (i,j)-th entry is binomial(i,j)*7^(i-j)*2^j.

A038279 Triangle whose (i,j)-th entry is binomial(i,j)*8^(i-j)*1^j.

Odd powers of 3

none found yet.

Powers of 6

A013612 Triangle of coefficients in expansion of (1+5x)^n.

A038210 Triangle whose (i,j)-th entry is binomial(i,j)*2^(i-j)*4^j.

A038221 Triangle whose (i,j)-th entry is binomial(i,j)*3^(i-j)*3^j.

A038232 Triangle whose (i,j)-th entry is binomial(i,j)*4^(i-j)*2^j.

A038243 Triangle whose (i,j)-th entry is binomial(i,j)*5^(i-j)*1^j.

partial match

A144879 Partition number array, called M31(-5), related to A049411(n,m)= S1(-5;n,m) (generalized Stirling triangle).

coincidence for the first three rows if interpreted as a linear triangle, but the row lengths are the partition numbers

A032362 Numbers n such that 25*2^n+1 is prime.

Powers of 12

A013618 Triangle of coefficients in expansion of (1+11x)^n.

A013626 Triangle of coefficients in expansion of (5+7x)^n.

A038216 Triangle whose (i,j)-th entry is binomial(i,j)*2^(i-j)*10^j.

A038227 Triangle whose (i,j)-th entry is binomial(i,j)*3^(i-j)*9^j.

A038238 Triangle whose (i,j)-th entry is binomial(i,j)*4^(i-j)*8^j.

A038260 Triangle read by rows: T(n,k) = binomial(n,k)*6^(n-k)*6^k, 0<=k<=n.

A038271 Triangle whose (i,j)-th entry is binomial(i,j)*7^(i-j)*5^j.

A038282 Triangle whose (i,j)-th entry is binomial(i,j)*8^(i-j)*4^j.

A038293 Triangle whose (i,j)-th entry is binomial(i,j)*9^(i-j)*3^j.

A038304 Triangle whose (i,j)-th entry is binomial(i,j)*10^(i-j)*2^j.

A038315 Triangle whose (i,j)-th entry is binomial(i,j)*11^(i-j)*1^j.