A195339 Expansion of 1/(1-4*x+2*x^3+x^4).

1, 4, 16, 62, 239, 920, 3540, 13620, 52401, 201604, 775636, 2984122, 11480879, 44170640, 169938680, 653808840, 2515413201, 9677604804, 37232862856, 143246816182, 551116641919, 2120323237160, 8157566453420, 31384785713660, 120747379738401

Offset: 0

Author

Bruno Berselli, Sep 16 2011

Keywords

• nonn
• easy

Links

• Bruno Berselli, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,0,-2,-1).

Crossrefs

Cf. A185962 (gives the coefficients of the denominator of the g.f., row 5 of its triangular array). Sequences likewise related to A185962: A000007 (row 1), A000012 (row 2), A000129 (row 3) and A006190 (row 4).

Programs

Magma

m:=25; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-4*x+2*x^3+x^4)));

Mathematica

CoefficientList[Series[1/(1-4x+2x^3+x^4),{x,0,30}],x] (* or *) LinearRecurrence[{4,0,-2,-1},{1,4,16,62},30] (* Harvey P. Dale, Dec 02 2011 *)

Maxima

makelist(coeff(taylor(1/(1-4*x+2*x^3+x^4), x, 0, n), x, n), n, 0, 24);

PARI

Vec(1/(1-4*x+2*x^3+x^4)+O(x^25))

Formula

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

a(n) = 4*a(n-1)-2*a(n-3)-a(n-4).