A056590 Fourth column sequence of triangle A056588.

1, 7, 53, 318, 1784, 9288, 46233, 221859, 1036585, 4742650, 21350264, 94895016, 417562385, 1822824255, 7907350365, 34130697462, 146735898760, 628870859320, 2688466352825, 11470754475675, 48865641344081, 207913415718642

Offset: 0

Author

Wolfdieter Lang Jul 10 2000

Keywords

• nonn
• easy

Crossrefs

Cf. A000045, A056588, A000012, A000071, A056589.

Formula

a(n)= A056588(n+3, 3), n >= 0.

a(n)= 3^(n+4)-F(n+5)*2^(n+4)+(F(n+3)-2)*F(n+5)*F(n+4)/2; F(n)=A000045(n) (Fibonacci).

G.f.:(1-3*x+8*x^2-3*x^3-3*x^4-4*x^5)/((1+x)*(1-3*x)*(1+x-x^2)*(1-2*x-4*x^2)*(1-3*x+x^2)*(1-4*x-x^2)).