A135094 a(n) = 2*a(n-1) + 2*a(n-2) - 4*a(n-3) with n>2, a(0)=0, a(1)=1, a(2)=3.

0, 1, 3, 8, 18, 40, 84, 176, 360, 736, 1488, 3008, 6048, 12160, 24384, 48896, 97920, 196096, 392448, 785408, 1571328, 3143680, 6288384, 12578816, 25159680, 50323456, 100651008, 201310208, 402628608, 805273600, 1610563584, 3221159936

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,2,-4).

Formula

From R. J. Mathar, Feb 15 2008: (Start)

O.g.f.: -3/(2*(2*x-1)) + (4*x+3)/(2*(2*x^2-1)).

a(n) = 3*2^(n-1) - A063759(n+1)/2. (End)

From Colin Barker, Sep 23 2016: (Start)

a(n) = 3*2^(n-1) - 3*2^(n/2-1) for n even.

a(n) = 3*2^(n-1) - 2^((n+1)/2) for n odd. (End)

Mathematica

LinearRecurrence[{2, 2, -4}, {0, 1, 3}, 50] (* G. C. Greubel, Sep 22 2016 *)

Prog

(Magma) I:=[0, 1, 3]; [n le 3 select I[n] else 2*Self(n-1)+2*Self(n-2)-4*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Sep 23 2016

Crossrefs

Cf. A026635, A026657.

Sequence in context: A335464 A369733 A026635 * A026657 A036384 A294591

Adjacent sequences: A135091 A135092 A135093 * A135095 A135096 A135097

Keyword

nonn,easy

Author

Paul Curtz, Feb 12 2008

Extensions

More terms from R. J. Mathar, Feb 15 2008

Status

approved