A113345 Matrix square of triangle A113340.

1, 2, 1, 5, 6, 1, 19, 39, 10, 1, 113, 327, 105, 14, 1, 966, 3556, 1315, 203, 18, 1, 10958, 48659, 19875, 3367, 333, 22, 1, 156700, 812462, 357860, 64750, 6867, 495, 26, 1, 2727794, 16136404, 7547602, 1435497, 160005, 12199, 689, 30, 1

Offset

0,2

Comments

Transforms column k of triangle A113340 into column k+1 of A113340. Also transforms column k of triangle A113350 into column k+1 of A113350.

Links

Table of n, a(n) for n=0..44.

Example

Matrix square A113340^2 starts:
1;
2,1;
5,6,1;
19,39,10,1;
113,327,105,14,1;
966,3556,1315,203,18,1;
10958,48659,19875,3367,333,22,1;
156700,812462,357860,64750,6867,495,26,1;
2727794,16136404,7547602,1435497,160005,12199,689,30,1; ...

Prog

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

Crossrefs

Cf. A113340, A113346 (column 0), A113347 (column 1), A113348 (column 2), A113349 (column 3); A113350.

Sequence in context: A124575 A178121 A302595 * A078123 A342968 A323312

Adjacent sequences: A113342 A113343 A113344 * A113346 A113347 A113348

Keyword

nonn,tabl

Author

Paul D. Hanna, Nov 08 2005

Status

approved