A016205 Expansion of g.f. 1/((1-x)*(1-2*x)*(1-10*x)).

1, 13, 137, 1385, 13881, 138873, 1388857, 13888825, 138888761, 1388888633, 13888888377, 138888887865, 1388888886841, 13888888884793, 138888888880697, 1388888888872505, 13888888888856121, 138888888888823353, 1388888888888757817, 13888888888888626745, 138888888888888364601

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (13,-32,20).

Crossrefs

Cf. A002275, A016134.

Programs

PARI

Vec(1/(1-13*x+32*x^2-20*x^3) + O(x^21)) \\ Elmo R. Oliveira, Mar 26 2025

Formula

a(n) = (25*10^n - 9*2^n + 2)/18. - Bruno Berselli, Feb 09 2011

a(n) = 10*a(n-1) + 2^(n+1) - 1 if n > 0; a(0)=1. - Vincenzo Librandi, Feb 09 2011

From Elmo R. Oliveira, Mar 26 2025: (Start)

E.g.f.: exp(x)*(25*exp(9*x) - 9*exp(x) + 2)/18.

a(n) = 13*a(n-1) - 32*a(n-2) + 20*a(n-3).

a(n) = A016134(n+1) - A002275(n+2). (End)

Extensions

More terms from Elmo R. Oliveira, Mar 26 2025