A114150 Triangle, read by rows, given by the product R^2*Q^-1 = Q^3*P^-2 using triangular matrices P=A113370, Q=A113381, R=A113389.

1, 4, 1, 28, 7, 1, 326, 91, 10, 1, 5702, 1722, 190, 13, 1, 136724, 43764, 4945, 325, 16, 1, 4226334, 1415799, 163705, 10751, 496, 19, 1, 161385532, 56096733, 6617605, 437723, 19896, 703, 22, 1

Offset: 0

Author

Paul D. Hanna, Nov 15 2005

Keywords

• nonn
• tabl

Comments

Complementary to A114151, which gives R^-2*Q^3 = Q^-1*P^2.

Examples

			Triangle R^2*Q^-1 = Q^3*P^-2 begins:
1;
4,1;
28,7,1;
326,91,10,1;
5702,1722,190,13,1;
136724,43764,4945,325,16,1;
4226334,1415799,163705,10751,496,19,1; ...
Compare to P (A113370):
1;
1,1;
1,4,1;
1,28,7,1;
1,326,91,10,1;
1,5702,1722,190,13,1; ...
Thus R^2*Q^-1 = Q^3*P^-2 equals P shift left one column.
		

Crossrefs

Cf. A113370 (P), A113381 (Q), A113389 (R); A114151 (R^-2*Q^3=Q^-1*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).

Programs

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^2*Q^-1)[n+1,k+1]