%I #2 Mar 30 2012 18:37:08
%S 1,3,1,21,12,1,208,156,21,1,2637,2350,399,30,1,40731,41034,8029,750,
%T 39,1,742620,821562,177198,18865,1209,48,1,15624420,18631332,4317936,
%U 502335,36478,1776,57,1,372892266,473187270,115949841,14390880,1136811
%N Matrix cube of triangle U = A136228, read by rows.
%F Column k of U^3 (this triangle) = column 2 of P^(3k+1), where P = triangle A136220.
%e This triangle, U^3, begins:
%e 1;
%e 3, 1;
%e 21, 12, 1;
%e 208, 156, 21, 1;
%e 2637, 2350, 399, 30, 1;
%e 40731, 41034, 8029, 750, 39, 1;
%e 742620, 821562, 177198, 18865, 1209, 48, 1;
%e 15624420, 18631332, 4317936, 502335, 36478, 1776, 57, 1;
%e 372892266, 473187270, 115949841, 14390880, 1136811, 62488, 2451, 66, 1;
%e where column 0 of U^3 = column 2 of P = A136220.
%o (PARI) {T(n,k)=local(P=Mat(1),U=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])))));(U^3)[n+1,k+1]}
%Y Cf. A136223 (column 0); related tables: A136220 (P), A136228 (U), A136230 (V), A136231 (W=P^3), A136233 (U^2).
%K nonn,tabl
%O 0,2
%A _Paul D. Hanna_, Feb 07 2008