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Row sums of triangle A185628.
3

%I #5 Mar 30 2012 18:37:26

%S 1,4,10,32,137,766,5382,46022,467206,5519252,74629263,1139283601,

%T 19411643752,365595475542,7548810986515,169681672611815,

%U 4126880020198630,108026180912533227,3029184083924476085,90617948406514693702,2881333799993441893564,97057552263114611503090

%N Row sums of triangle A185628.

%C Triangle A185628 equals the matrix cube of triangle R = A185620, which satisfies: R^3 - R^2 + I = R shifted left one column.

%o (PARI) {a(n)=local(A=Mat(1), B); for(m=1, n+1, B=A^3-A^2+A^0; A=matrix(m+1, m+1); for(i=1, m+1, for(j=1, i, if(i<2|j==i, A[i, j]=1, if(j==1, A[i, j]=1, A[i, j]=B[i-1, j-1]))))); return(sum(k=1,n+1,(A^3)[n+1, k]))}

%Y Cf. A185620, A185628, A185629, A185630.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Sep 07 2011