A154252 Expansion of (1-x+8x^2)/((1-x)(1-2x)) .

1, 2, 12, 32, 72, 152, 312, 632, 1272, 2552, 5112, 10232, 20472, 40952, 81912, 163832, 327672, 655352, 1310712, 2621432, 5242872, 10485752, 20971512, 41943032, 83886072, 167772152, 335544312, 671088632, 1342177272, 2684354552, 5368709112, 10737418232

Offset: 0

Author

Philippe Deléham, Jan 05 2009

Keywords

• nonn
• easy

Comments

Binomial transform of 1,1,9,1,9,1,9,1,9,1,9,1,9,1,9,...

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, A154251

Programs

Mathematica

Join[{1},LinearRecurrence[{3,-2},{2,12},40]]  (* Harvey P. Dale, Dec 30 2014 *)
Join[{1},Table[5*2^n - 8, {n,1,25}]] (* G. C. Greubel, Sep 08 2016 *)

PARI

Vec((1-x+8*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)=12.

a(n) = 2*a(n-1) + 8, n>1, with a(0)=1, a(1)=2.

a(n) = 10*2^(n-1) - 8, n>=1, with a(0)=1.

E.g.f.: 5*exp(2*x) - 8*exp(x) + 4. - G. C. Greubel, Sep 08 2016

Extensions

Two terms corrected by Johannes W. Meijer, May 26 2011