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

Author

Paul D. Hanna, Nov 08 2005

Keywords

• nonn
• tabl

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.

Examples

			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; ...
		

Crossrefs

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

Programs

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]