A154251 Expansion of (1-x+7x^2)/((1-x)(1-2x)).

1, 2, 11, 29, 65, 137, 281, 569, 1145, 2297, 4601, 9209, 18425, 36857, 73721, 147449, 294905, 589817, 1179641, 2359289, 4718585, 9437177, 18874361, 37748729, 75497465, 150994937, 301989881, 603979769, 1207959545, 2415919097

Offset: 0

Author

Philippe Deléham, Jan 05 2009

Keywords

• nonn
• easy

Comments

Binomial transform of 1,1,8,1,8,1,8,1,8,1,8,1,8,1,8,...

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-2).

Crossrefs

Cf.: A094373, A000079, A083329, A095121, A154117, A131128, A154118, A131130

Programs

Mathematica

Join[{1},LinearRecurrence[{3,-2},{2,11}, 25]] (* or *) Join[{1},Table[9*2^(n-1) - 7, {n,1,25}]] (* G. C. Greubel, Sep 08 2016 *)

PARI

Vec((1-x+7*x^2)/((1-x)*(1-2*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Formula

a(n) = 3*a(n-1) - 2*a(n-2), n>2, with a(0)=1, a(1)=2, a(2)=11.

a(n) = 9*2^(n-1) - 7, n>0, with a(0)=1.

a(n) = 2*a(n-1) + 7, n>1, with a(0)=1, a(1)=2.

From G. C. Greubel, Sep 08 2016: (Start)

a(n) = 9*2^(n-1) - 7 for n >= 1.

E.g.f.: (1/2)*(9*exp(2*x) - 14*exp(x) + 7). (End)