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A113374
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Triangle, read by rows, equal to the matrix square of A113370. Also given by the product: P^2 = Q*(R^-2)*Q^3, using triangular matrices P=A113370, Q=A113381 and R=A113389.
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7
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1, 2, 1, 6, 8, 1, 37, 84, 14, 1, 429, 1296, 252, 20, 1, 7629, 27850, 5957, 510, 26, 1, 185776, 784146, 179270, 16180, 858, 32, 1, 5817106, 27630378, 6641502, 623115, 34125, 1296, 38, 1, 224558216, 1177691946, 294524076, 28470525, 1599091, 61952
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| Column k of A113370^2 = column 0 of A113381^(3*k+1).
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EXAMPLE
| Triangle A113370^2 begins:
1;
2,1;
6,8,1;
37,84,14,1;
429,1296,252,20,1;
7629,27850,5957,510,26,1;
185776,784146,179270,16180,858,32,1;
5817106,27630378,6641502,623115,34125,1296,38,1;
224558216,1177691946,294524076,28470525,1599091,61952,1824,44,1;
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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); (A^2)[n+1, k+1]}
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CROSSREFS
| Cf. A113370, A113381, A113389; A113375 (column 0), A113376 (column 1), A113377 (column 2); A113378 (P^3), A113387 (Q^3).
Sequence in context: A110608 A190015 A112007 * A136470 A138510 A026215
Adjacent sequences: A113371 A113372 A113373 * A113375 A113376 A113377
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KEYWORD
| nonn,tabl
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Nov 14 2005
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