cp's OEIS Frontend

A113384 Triangle, read by rows, equal to the matrix square of A113381. Also given by: Q^2 = R*P = R*Q*(R^-2)*Q*R = P*Q*(P^-2)*Q*P, using triangular matrices P=A113370, Q=A113381 and R=A113389.

%I A113384 #6 Jun 13 2017 23:29:58
%S A113384 1,4,1,22,10,1,212,130,16,1,3255,2365,328,22,1,70777,57695,8640,616,
%T A113384 28,1,2022897,1798275,284356,21197,994,34,1,72375484,68931064,
%U A113384 11358500,875424,42196,1462,40,1,3130502129,3155772612,537277044,42499204
%N A113384 Triangle, read by rows, equal to the matrix square of A113381. Also given by: Q^2 = R*P = R*Q*(R^-2)*Q*R = P*Q*(P^-2)*Q*P, using triangular matrices P=A113370, Q=A113381 and R=A113389.
%e A113384 Triangle A113381^2 begins:
%e A113384 1;
%e A113384 4,1;
%e A113384 22,10,1;
%e A113384 212,130,16,1;
%e A113384 3255,2365,328,22,1;
%e A113384 70777,57695,8640,616,28,1;
%e A113384 2022897,1798275,284356,21197,994,34,1;
%e A113384 72375484,68931064,11358500,875424,42196,1462,40,1;
%e A113384 3130502129,3155772612,537277044,42499204,2094365,73797,2020,46,1;
%o A113384 (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); (matrix(#A,#A,r,c,if(r>=c,(A^(3*c-1))[r-c+1,1]))^2)[n+1,k+1]
%Y A113384 Cf. A113381, A113385 (column 0), A113386 (column 1); A113370, A113389.
%K A113384 nonn,tabl
%O A113384 0,2
%A A113384 _Paul D. Hanna_, Nov 14 2005