A189426 Expansion of (x^2)/(1-2*x-x^2+x^3)^2

0, 0, 1, 4, 14, 42, 119, 322, 847, 2180, 5521, 13804, 34160, 83818, 204204, 494494, 1191227, 2856666, 6823334, 16240714, 38534657, 91175154, 215179125, 506670394, 1190534467, 2792076392, 6536567296, 15278103876, 35656587624, 83101366684

Offset

0,4

Comments

Convolution of A006054={0,0,1,2,5,11,25,56,126,...} with itself.

For n=0,1,2,..., partial sums are given by Sum_{k=0..n} a(k)=A189427(n), where A189427={0,0,1,5,19,61,180,...}.

Links

Table of n, a(n) for n=0..29.

Index entries for linear recurrences with constant coefficients, signature (4, -2, -6, 3, 2, -1).

Formula

G.f.: (x^2)/(1-2*x-x^2+x^3)^2.

a(n)=4*a(n-1)-2*a(n-2)-6*a(n-3)+3*a(n-4)+2*a(n-5)-a(n-6), n>=6.

Mathematica

CoefficientList[Series[x^2/(1-2x-x^2+x^3)^2, {x, 0, 40}], x] (* or *) LinearRecurrence[{4, -2, -6, 3, 2, -1}, {0, 0, 1, 4, 14, 42}, 40] (* Harvey P. Dale, Feb 29 2012 *)

Prog

(PARI) Vec((x^2)/(1-2*x-x^2+x^3)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Crossrefs

Cf. A006054, A189427.

Sequence in context: A124617 A124618 A189052 * A007076 A135483 A095377

Adjacent sequences: A189423 A189424 A189425 * A189427 A189428 A189429

Keyword

nonn,easy

Author

L. Edson Jeffery, Apr 22 2011

Status

approved