A109286 - OEIS

%I #3 Mar 30 2012 18:36:49

%S 1,2,6,25,146,1074,9247,89618,956106,11066959,137531624,1820347008,

%T 25499542444,376098118280,5815744322556,93946244699173,

%U 1580463050838884,27616009578136506,500029604169802336,9362566904514285044

%N Row sums of triangle A109282.

%C Triangular matrix T=A109282 satisfies: T(n,k) = [T^3](n-1,k) for n>k+1>=1, with T(n,n) = 1 and T(n+1,n) = n+1 for n>=0; also, T^(m+3) = SHIFT_UP(T^(m+1) - T^m) - D*T^m for all m where diagonal matrix D = [0,1,2,3,...] and SHIFT_UP shifts each column up 1 row.

%o (PARI) {a(n)=local(M=matrix(n+1,n+1));M=M^0;for(i=1,n, M=matrix(n+1,n+1,r,c,if(r>=c,if(r==c,1,if(r==c+1,c,(M^3)[r-1,c]))))); return(sum(k=0,n,M[n+1,k+1]))}

%Y Cf. A109155, A109282 (triangle), A109283 (column 0), A109284 (column 1), A109285 (column 2).

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jun 24 2005