A038990 Expansion of (1-x-x^2+2*x^3) / ((1-x)*(1+x)*(1-3*x+x^2)).

1, 2, 5, 14, 37, 98, 257, 674, 1765, 4622, 12101, 31682, 82945, 217154, 568517, 1488398, 3896677, 10201634, 26708225, 69923042, 183060901, 479259662, 1254718085, 3284894594, 8599965697, 22515002498, 58945041797, 154320122894, 404015326885, 1057725857762

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,0,-3,1).

Formula

a(n) = -1/2-(-1)^n/10+4*(2*A001906(n+1)-3*A001906(n))/5. - R. J. Mathar, Mar 31 2011

a(0)=1, a(1)=2, a(2)=5, a(3)=14, a(n)=3*a(n-1)-3*a(n-3)+a(n-4). - Harvey P. Dale, Feb 17 2012

a(n) = (-1)*(2^(-1-n)*((-2)^n + 5*2^n - 8*(3-sqrt(5))^n - 8*(3+sqrt(5))^n)) / 5. - Colin Barker, Jul 16 2017

Maple

A001906 := proc(n) combinat[fibonacci](2*n) ; end proc:
A038990 := proc(n) -1/2-(-1)^n/10+4*(2*A001906(n+1)-3*A001906(n))/5 ; end proc: # R. J. Mathar, Mar 31 2011

Mathematica

CoefficientList[Series[(1-x-x^2+2x^3)/((1-x)(1+x)(1-3x+x^2)), {x, 0, 30}], x] (* or *) LinearRecurrence[{3, 0, -3, 1}, {1, 2, 5, 14}, 30] (* Harvey P. Dale, Feb 17 2012 *)

Prog

(PARI) Vec((1-x-x^2+2*x^3)/((1-x)*(1+x)*(1-3*x+x^2))+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012

Crossrefs

Sequence in context: A030016 A248733 A099485 * A355387 A077938 A077987

Adjacent sequences: A038987 A038988 A038989 * A038991 A038992 A038993

Keyword

nonn,easy

Author

Colin Mallows

Status

approved