A113988 Triangle, read by rows, equal to the matrix square of A113983.

1, 2, 1, 4, 4, 1, 8, 12, 6, 1, 18, 36, 26, 8, 1, 46, 116, 108, 46, 10, 1, 136, 416, 468, 248, 72, 12, 1, 464, 1680, 2194, 1366, 480, 104, 14, 1, 1818, 7656, 11294, 7976, 3222, 828, 142, 16, 1, 8122, 39256, 64152, 50186, 22590, 6568, 1316, 186, 18, 1

Offset

0,2

Links

Table of n, a(n) for n=0..54.

Formula

G.f.: A(x, y) = ( (1-x*y)*GF(A113983) - 1/(1-x) )/(x^2*y) (cf. A113983). T(n, 0) = T(n-2, 0) + T(n-1, 1) + 2.

Example

Triangle begins:
1;
2,1;
4,4,1;
8,12,6,1;
18,36,26,8,1;
46,116,108,46,10,1;
136,416,468,248,72,12,1;
464,1680,2194,1366,480,104,14,1;
1818,7656,11294,7976,3222,828,142,16,1;
8122,39256,64152,50186,22590,6568,1316,186,18,1;
41076,225348,402072,342584,168296,53816,12056,1968,236,20,1; ...
Notice that T(n+1,0) = T(n,1) + T(n-1,0) + 2:
T(7,0) = 464 = T(6,1) + T(5,0) = 416 + 46 + 2;
T(8,0) = 1818 = T(7,1) + T(6,0) = 1680 + 136 + 2.

Prog

(PARI) T(n, k)=local(A, B); A=Mat(1); for(m=2, n+1, B=matrix(m, m); for(i=1, m, for(j=1, i, if(i<3 || j==1 || j==i, B[i, j]=1, B[i, j]=A[i-1, j-1]+(A^2)[i-2, j-1] ); )); A=B); (A^2)[n+1, k+1]

Crossrefs

Cf. A113989 (column 0), A113990 (column 1), A113991 (column 2), A113992 (column 3); A113983, A113993.

Sequence in context: A134395 A065109 A038207 * A209240 A263989 A202710

Adjacent sequences: A113985 A113986 A113987 * A113989 A113990 A113991

Keyword

nonn,tabl

Author

Paul D. Hanna, Nov 12 2005

Status

approved