A154117 Expansion of (1 - x + 3*x^2)/((1-x)*(1-2*x)).

1, 2, 7, 17, 37, 77, 157, 317, 637, 1277, 2557, 5117, 10237, 20477, 40957, 81917, 163837, 327677, 655357, 1310717, 2621437, 5242877, 10485757, 20971517, 41943037, 83886077, 167772157, 335544317, 671088637, 1342177277, 2684354557

Offset: 0

Author

Vladimir Joseph Stephan Orlovsky, Dec 15 2008

Keywords

• nonn
• easy

Comments

Binomial transform of 1,1,4,1,4,1,4,1,4,1,4,1,4,1,4,... - Philippe Deleham, Jan 05 2009

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, A131128, A131130.

Programs

Magma

[1] cat [5*2^n-3 : n in [0..30]]; // Vincenzo Librandi, Nov 11 2011

Mathematica

Join[{1}, Table[ 5*2^(n - 1) - 3, {n, 1, 10}]] (* or *) Join[{1, 2, 7}, LinearRecurrence[{3, -2}, {17, 37}, 10]] (* G. C. Greubel, Sep 02 2016 *)

PARI

a(n)=if(n, 5<<(n-1)-3, 1) \\ Charles R Greathouse IV, Sep 02 2016

Formula

From Philippe Deléham, Jan 05 2009: (Start)

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

a(n) = 2*a(n-1) + 3, n > 1.

a(n) = 5*2^(n-1) - 3, n >= 1. (End)

E.g.f.: (1/2)*(3 - 6*exp(x) + 5*exp(2*x)). - G. C. Greubel, Sep 02 2016

Extensions

a(0) added by Philippe Deléham, Jan 05 2009