OFFSET
0,2
FORMULA
Column k of W^2 (this triangle) = column 1 of W^(k+1), where W = P^3 and P = triangle A136220.
EXAMPLE
This triangle, W^2, begins:
1;
6, 1;
48, 12, 1;
495, 150, 18, 1;
6338, 2160, 306, 24, 1;
97681, 36103, 5643, 516, 30, 1;
1767845, 694079, 115917, 11592, 780, 36, 1;
36839663, 15164785, 2657946, 282122, 20655, 1098, 42, 1;
870101407, 372225541, 67708113, 7502470, 580780, 33480, 1470, 48, 1; ...
where column 0 of W^2 = column 1 of W = triangle A136231.
PROG
(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]}
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Feb 07 2008
STATUS
approved