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

Author

L. Edson Jeffery, Apr 22 2011

Keywords

• nonn
• easy

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

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

Crossrefs

Cf. A006054, A189427.

Programs

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 *)

PARI

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

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.