A016163 Expansion of 1/((1-5*x)*(1-9*x)).

1, 14, 151, 1484, 13981, 128954, 1176211, 10664024, 96366841, 869254694, 7833057871, 70546348964, 635161281301, 5717672234834, 51465153629131, 463216900240304, 4169104690053361, 37522705149933374, 337708161046665991

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (14,-45).

Crossrefs

Cf. A016142, A016161.

Programs

Magma

[(9^(n+1) - 5^(n+1))/4: n in [0..30]]; // G. C. Greubel, Nov 09 2024

Mathematica

Table[(9^(n+1) - 5^(n+1))/4, {n,0,30}] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2011 *)

SageMath

def A016163(n): return (9^(n+1) - 5^(n+1))/4
[A016163(n) for n in range(31)] # G. C. Greubel, Nov 09 2024

Formula

a(n) = ((7+sqrt4)^n - (7-sqrt4)^n)/4. Offset 1. a(3)=151. - Al Hakanson (hawkuu(AT)gmail.com), Dec 31 2008

a(n) = 14*a(n-1) - 45*a(n-2). - Philippe Deléham, Jan 01 2009

a(0)=1, a(n) = 9*a(n-1) + 5^n. - Vincenzo Librandi, Feb 09 2011

From G. C. Greubel, Nov 09 2024: (Start)

a(n) = (9^(n+1) - 5^(n+1))/4.

E.g.f.: (1/4)*(9*exp(9*x) - 5*exp(5*x)). (End)