A113378 Triangle, read by rows, equal to the matrix cube of A113370.

1, 3, 1, 15, 12, 1, 136, 168, 21, 1, 1998, 3190, 483, 30, 1, 41973, 80136, 13615, 960, 39, 1, 1166263, 2553162, 469476, 35785, 1599, 48, 1, 40747561, 99579994, 19419225, 1562220, 74074, 2400, 57, 1, 1726907675, 4624245724, 944233801, 79072620

Offset: 0

Author

Paul D. Hanna, Nov 14 2005

Keywords

• nonn
• tabl

Examples

			Triangle A113370^3 begins:
1;
3,1;
15,12,1;
136,168,21,1;
1998,3190,483,30,1;
41973,80136,13615,960,39,1;
1166263,2553162,469476,35785,1599,48,1;
40747561,99579994,19419225,1562220,74074,2400,57,1;
1726907675,4624245724,944233801,79072620,3908034,132856,3363,66,1;
		

Crossrefs

Cf. A113370, A113389, A113379 (column 0), A113380 (column 1).

Programs

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

Formula

Column k of A113370^3 = column 0 of A113389^(3*k+1) for k>=0.