A114151 Triangle, read by rows, given by the product R^-2*Q^3 = Q^-1*P^2 using triangular matrices P=A113370, Q=A113381, R=A113389.

1, 0, 1, 0, 3, 1, 0, 15, 6, 1, 0, 136, 66, 9, 1, 0, 1998, 1091, 153, 12, 1, 0, 41973, 24891, 3621, 276, 15, 1, 0, 1166263, 737061, 110637, 8482, 435, 18, 1, 0, 40747561, 27110418, 4176549, 323874, 16430, 630, 21, 1

Offset

0,5

Comments

Complementary to A114150, which gives R^2*Q^-1 = Q^3*P^-2.

Links

Table of n, a(n) for n=0..44.

Example

Triangle R^-2*Q^3 = Q^-1*P^2 begins:
1;
0,1;
0,3,1;
0,15,6,1;
0,136,66,9,1;
0,1998,1091,153,12,1;
0,41973,24891,3621,276,15,1; ...
Compare to R (A113389):
1;
3,1;
15,6,1;
136,66,9,1;
1998,1091,153,12,1;
41973,24891,3621,276,15,1; ...
Thus R^-2*Q^3 = Q^-1*P^2 equals R shift right 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])); (Q^-1*P^2)[n+1, k+1]

Crossrefs

Cf. A113370 (P), A113381 (Q), A113389 (R); A114150 (R^2*Q^-1=Q^3*P^-2), A114152 (R^3*P^-1), 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: A137431 A131222 A228334 * A243098 A360177 A241981

Adjacent sequences: A114148 A114149 A114150 * A114152 A114153 A114154

Keyword

nonn,tabl

Author

Paul D. Hanna, Nov 15 2005

Status

approved