A113380 -id:A113380 - cp's OEIS frontend

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

Paul D. Hanna, Nov 14 2005

			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;

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

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]

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

A113379 Column 0 of triangle A113378, also equals column 0 of A113389.

Original entry on oeis.org

1, 3, 15, 136, 1998, 41973, 1166263, 40747561, 1726907675, 86421647389, 5002021986418, 329382745551946, 24351172588548270, 1999205882982496161, 180613538916429940159, 17817366508243503227269

Offset: 0

Paul D. Hanna, Nov 14 2005

nonn

Cf. A113378, A113370, A113389, A113380 (column 1).

a(n)=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+1,1]

A113378 equals the matrix cube of A113370, which has the property: column k of A113370^3 = column 0 of A113389^(3*k+1) for k>=0.

cp's OEIS Frontend

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

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