A109285 Column 2 of triangle A109282.

1, 3, 9, 63, 492, 4545, 46935, 530562, 6485211, 84764205, 1176089460, 17217555903, 264670166322, 4255132537038, 71307312415452, 1242006842599569, 22428783284638182, 419022897322142115, 8083317501072692514

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..18.

Prog

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

Crossrefs

Cf. A109155, A109282 (triangle), A109283 (column 0), A109284 (column 1), A109286 (row sums).

Sequence in context: A085435 A121696 A108557 * A245165 A091760 A144525

Adjacent sequences: A109282 A109283 A109284 * A109286 A109287 A109288

Keyword

nonn

Author

Paul D. Hanna, Jun 24 2005

Status

approved