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A113374 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.

%I A113374 #6 Jun 13 2017 23:21:04
%S A113374 1,2,1,6,8,1,37,84,14,1,429,1296,252,20,1,7629,27850,5957,510,26,1,
%T A113374 185776,784146,179270,16180,858,32,1,5817106,27630378,6641502,623115,
%U A113374 34125,1296,38,1,224558216,1177691946,294524076,28470525,1599091,61952
%N A113374 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.
%F A113374 Column k of A113370^2 = column 0 of A113381^(3*k+1).
%e A113374 Triangle A113370^2 begins:
%e A113374 1;
%e A113374 2,1;
%e A113374 6,8,1;
%e A113374 37,84,14,1;
%e A113374 429,1296,252,20,1;
%e A113374 7629,27850,5957,510,26,1;
%e A113374 185776,784146,179270,16180,858,32,1;
%e A113374 5817106,27630378,6641502,623115,34125,1296,38,1;
%e A113374 224558216,1177691946,294524076,28470525,1599091,61952,1824,44,1;
%o A113374 (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]
%Y A113374 Cf. A113370, A113381, A113389; A113375 (column 0), A113376 (column 1), A113377 (column 2); A113378 (P^3), A113387 (Q^3).
%K A113374 nonn,tabl
%O A113374 0,2
%A A113374 _Paul D. Hanna_, Nov 14 2005