A114154 Triangle, read by rows, given by the product R^3*Q^-2 using triangular matrices Q=A113381, R=A113389.

1, 5, 1, 45, 8, 1, 635, 120, 11, 1, 12815, 2556, 231, 14, 1, 343815, 71548, 6556, 378, 17, 1, 11651427, 2508528, 233706, 13391, 561, 20, 1, 480718723, 106427700, 10069521, 579047, 23817, 780, 23, 1

Offset

0,2

Comments

Complementary to A114155, which gives Q^-2*P^3.

Links

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

Example

Triangle R^3*Q^-2 begins:
1;
5,1;
45,8,1;
635,120,11,1;
12815,2556,231,14,1;
343815,71548,6556,378,17,1; ...
Compare to Q (A113381):
1;
2,1;
6,5,1;
37,45,8,1;
429,635,120,11,1;
7629,12815,2556,231,14,1; ...
Thus R^3*Q^-2 equals Q 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*Q^-2)[n+1, k+1]

Crossrefs

Cf. A113394 (R^3), A113370 (P), A113381 (Q), A113389 (R); A114150 (R^2*Q^-1=Q^3*P^-2), A114151 (R^-2*Q^3=Q^-1*P^2), A114152 (R^3*P^-1), A114153 (R^-1*P^3), A114155 (Q^-2*P^3); A114156 (P^-1), A114158 (Q^-1), A114159 (R^-1).

Sequence in context: A134274 A134275 A264774 * A297899 A134273 A048897

Adjacent sequences: A114151 A114152 A114153 * A114155 A114156 A114157

Keyword

nonn,tabl

Author

Paul D. Hanna, Nov 15 2005

Status

approved