A119457 Triangle read by rows: T(n,1)=n, T(n,2)=(n-1)*2 for n>1 and T(n,k)=T(n-1,k-1)+T(n-2,k-2) for 2<k<=n.

1, 2, 2, 3, 4, 3, 4, 6, 6, 5, 5, 8, 9, 10, 8, 6, 10, 12, 15, 16, 13, 7, 12, 15, 20, 24, 26, 21, 8, 14, 18, 25, 32, 39, 42, 34, 9, 16, 21, 30, 40, 52, 63, 68, 55, 10, 18, 24, 35, 48, 65, 84, 102, 110, 89, 11, 20, 27, 40, 56, 78, 105, 136, 165, 178, 144, 12, 22, 30, 45, 64, 91, 126, 170, 220, 267, 288, 233

Offset

1,2

Comments

Row sums give A001891; central terms give A023607;

T(n,1) = n;

T(n,2) = A005843(n-1) for n>1;

T(n,3) = A008585(n-2) for n>2;

T(n,4) = A008587(n-3) for n>3;

T(n,5) = A008590(n-4) for n>4;

T(n,6) = A008595(n-5) for n>5;

T(n,7) = A008603(n-6) for n>6;

T(n,n-6) = A022090(n-5) for n>6;

T(n,n-5) = A022089(n-4) for n>5;

T(n,n-4) = A022088(n-3) for n>4;

T(n,n-3) = A022087(n-2) for n>3;

T(n,n-2) = A022086(n-1) for n>2;

T(n,n-1) = A006355(n+1) for n>1;

T(n,n) = A000045(n+1);

Links

Table of n, a(n) for n=1..78.

Eric Weisstein's World of Mathematics, Fibonacci Number

Formula

T(n,n) = (n+1)-th Fibonacci number, T(n,k) = (n-k+1)*T(k,k) for 1<=k<n.

Mathematica

T[n_, 1] := n;
T[n_ /; n > 1, 2] := 2 n - 2;
T[n_, k_] /; 2 < k <= n := T[n, k] = T[n - 1, k - 1] + T[n - 2, k - 2];
Table[T[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* Jean-François Alcover, Dec 01 2021 *)

Crossrefs

Sequence in context: A368310 A003991 A131923 * A241356 A065157 A235804

Adjacent sequences: A119454 A119455 A119456 * A119458 A119459 A119460

Keyword

nonn,tabl

Author

Reinhard Zumkeller, May 20 2006

Status

approved