A114152 Triangle, read by rows, given by the product R^3*P^-1 using triangular matrices P=A113370, R=A113389.

1, 8, 1, 84, 14, 1, 1296, 252, 20, 1, 27850, 5957, 510, 26, 1, 784146, 179270, 16180, 858, 32, 1, 27630378, 6641502, 623115, 34125, 1296, 38, 1, 1177691946, 294524076, 28470525, 1599091, 61952, 1824, 44, 1

Offset

0,2

Comments

Complementary to A114153, which gives R^-1*P^3.

Links

Table of n, a(n) for n=0..35.

Example

Triangular matrix R^3*P^-1 begins:
1;
8,1;
84,14,1;
1296,252,20,1;
27850,5957,510,26,1;
784146,179270,16180,858,32,1;
27630378,6641502,623115,34125,1296,38,1; ...
Compare to P^2 (A113374):
1;
2,1;
6,8,1;
37,84,14,1;
429,1296,252,20,1;
7629,27850,5957,510,26,1; ...
Thus R^3*P^-1 equals P^2 shift left one column.

Prog

(PARI) T(n, k)=local(P, Q, R, W); P=Mat(1); for(m=2, n+1, W=matrix(m, m); for(i=1, m, for(j=1, i, if(i<3 || j==i || j>m-1, W[i, j]=1, if(j==1, W[i, 1]=1, W[i, j]=(P^(3*j-2))[i-j+1, 1])); )); P=W); Q=matrix(#P, #P, r, c, if(r>=c, (P^(3*c-1))[r-c+1, 1])); R=matrix(#P, #P, r, c, if(r>=c, (P^(3*c))[r-c+1, 1])); (R^3*P^-1)[n+1, k+1]

Crossrefs

Cf. A113374 (P^2), A113370 (P), A113381 (Q), A113389 (R); A114150 (R^2*Q^-1=Q^3*P^-2), A114151 (R^-2*Q^3=Q^-1*P^2), A114153 (R^-1*P^3), A114154 (R^3*Q^-2), A114155 (Q^-2*P^3); A114156 (P^-1), A114158 (Q^-1), A114159 (R^-1).

Sequence in context: A260040 A051379 A143499 * A347111 A254933 A174503

Adjacent sequences: A114149 A114150 A114151 * A114153 A114154 A114155

Keyword

nonn,tabl

Author

Paul D. Hanna, Nov 15 2005

Status

approved