A109286 Row sums of triangle A109282.

1, 2, 6, 25, 146, 1074, 9247, 89618, 956106, 11066959, 137531624, 1820347008, 25499542444, 376098118280, 5815744322556, 93946244699173, 1580463050838884, 27616009578136506, 500029604169802336, 9362566904514285044

Offset

0,2

Comments

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.

Links

Table of n, a(n) for n=0..19.

Prog

(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]))}

Crossrefs

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

Sequence in context: A195259 A292748 A178087 * A009466 A372892 A348067

Adjacent sequences: A109283 A109284 A109285 * A109287 A109288 A109289

Keyword

nonn

Author

Paul D. Hanna, Jun 24 2005

Status

approved