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

0,2

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).

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).

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 *)

Prog

(PARI) Vec(1/(1-4*x+2*x^3+x^4)+O(x^25))
(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-4*x+2*x^3+x^4)));
(Maxima) makelist(coeff(taylor(1/(1-4*x+2*x^3+x^4), x, 0, n), x, n), n, 0, 24);

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).

Sequence in context: A085781 A113438 A268429 * A172025 A171278 A227438

Adjacent sequences: A195336 A195337 A195338 * A195340 A195341 A195342

Keyword

nonn,easy

Author

Bruno Berselli, Sep 16 2011

Status

approved