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A154117 Expansion of (1 - x + 3*x^2)/((1-x)*(1-2*x)). 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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).

FORMULA

Contribution 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

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 *)

PROG

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

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

CROSSREFS

Cf. A094373, A000079, A083329, A095121, A131128, A131130.

Sequence in context: A045380 A086321 A009302 * A173769 A067038 A209398

Adjacent sequences:  A154114 A154115 A154116 * A154118 A154119 A154120

KEYWORD

nonn,easy

AUTHOR

Vladimir Joseph Stephan Orlovsky, Dec 15 2008

EXTENSIONS

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

STATUS

approved

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Last modified December 7 09:38 EST 2016. Contains 278849 sequences.