%I #2 Mar 30 2012 18:37:08

%S 1,4,36,442,6742,122350,2571620,61426282,1643616044,48708655760,

%T 1583981114700,56090062706944,2148733943483128,88554674908328872,

%U 3907197406833303644,183780036631720987407,9180785177015520963631

%N Column 3 of triangle A136220; also equals column 0 of U^4 where U = A136228.

%C P = A136220 is a triangular matrix where column k of P^3 equals column 0 of P^(3k+3) such that column 0 of P^3 equals column 0 of P shift one place left.

%o (PARI) {a(n)=local(P=Mat(1),U,PShR);if(n==0,1,for(i=0,n+2, 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<#U,P[r,c], (U^c)[r-c+1,1]))));P[n+4,4])}

%Y Cf. A136220 (P), A136228 (U); other columns of P: A136221, A136222, A136223.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Dec 25 2007