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%I #2 Mar 30 2012 18:37:08
%S 1,6,1,48,12,1,495,150,18,1,6338,2160,306,24,1,97681,36103,5643,516,
%T 30,1,1767845,694079,115917,11592,780,36,1,36839663,15164785,2657946,
%U 282122,20655,1098,42,1,870101407,372225541,67708113,7502470,580780
%N Matrix square of triangle W = A136231; also equals P^6, where P = triangle A136220.
%F Column k of W^2 (this triangle) = column 1 of W^(k+1), where W = P^3 and P = triangle A136220.
%e This triangle, W^2, begins:
%e 1;
%e 6, 1;
%e 48, 12, 1;
%e 495, 150, 18, 1;
%e 6338, 2160, 306, 24, 1;
%e 97681, 36103, 5643, 516, 30, 1;
%e 1767845, 694079, 115917, 11592, 780, 36, 1;
%e 36839663, 15164785, 2657946, 282122, 20655, 1098, 42, 1;
%e 870101407, 372225541, 67708113, 7502470, 580780, 33480, 1470, 48, 1; ...
%e where column 0 of W^2 = column 1 of W = triangle A136231.
%o (PARI) {T(n,k)=local(P=Mat(1),U=Mat(1),W=Mat(1),PShR);if(n>0,for(i=0,n, PShR=matrix(#P,#P, r,c, if(r>=c,if(r==c,1,if(c==1,0,P[r-1,c-1])))); U=P*PShR^2; U=matrix(#P+1, #P+1, r,c, if(r>=c, if(r<#P+1,U[r,c], if(c==1,(P^3)[ #P,1],(P^(3*c-1))[r-c+1,1])))); P=matrix(#U, #U, r,c, if(r>=c, if(r<#R,P[r,c], (U^c)[r-c+1,1]))); W=P^3;));(W^2)[n+1,k+1]}
%Y Cf. A136221 (column 0); related tables: A136220 (P), A136228 (U), A136230 (V), A136231 (W), A136238 (W^3).
%K nonn,tabl
%O 0,2
%A _Paul D. Hanna_, Feb 07 2008
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