A113392 Triangle, read by rows, equal to the matrix square of triangle A113389. Also given by the matrix product: R^2 = Q^3*(P^-2)*Q, using triangular matrices P=A113370, Q=A113381 and R=A113389.

1, 6, 1, 48, 12, 1, 605, 186, 18, 1, 11196, 3892, 414, 24, 1, 280440, 106089, 12021, 732, 30, 1, 8981460, 3620379, 429345, 27152, 1140, 36, 1, 353283128, 149740555, 18386361, 1196910, 51445, 1638, 42, 1, 16567072675, 7316974618, 923656512

Offset

0,2

Links

Table of n, a(n) for n=0..38.

Example

Triangle A113389^2 begins:
1;
6,1;
48,12,1;
605,186,18,1;
11196,3892,414,24,1;
280440,106089,12021,732,30,1;
8981460,3620379,429345,27152,1140,36,1;
353283128,149740555,18386361,1196910,51445,1638,42,1;
16567072675,7316974618,923656512,61515702,2696010,87060,2226,48,1;

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==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); (matrix(#A, #A, r, c, if(r>=c, (A^(3*c))[r-c+1, 1]))^2)[n+1, k+1]

Crossrefs

Cf. A113389, A113388 (column 0), A113393 (column 1).

Sequence in context: A283151 A138192 A136235 * A113387 A290316 A090435

Adjacent sequences: A113389 A113390 A113391 * A113393 A113394 A113395

Keyword

nonn,tabl

Author

Paul D. Hanna, Nov 14 2005

Status

approved