A219751 Expansion of x^4*(2-3*x-x^2)/((1+x)*(1-2*x)^2).

0, 0, 0, 0, 2, 3, 8, 16, 36, 76, 164, 348, 740, 1564, 3300, 6940, 14564, 30492, 63716, 132892, 276708, 575260, 1194212, 2475804, 5126372, 10602268, 21903588, 45205276, 93206756, 192005916, 395196644, 812762908, 1670265060, 3430008604, 7038974180, 14435862300

Offset

0,5

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

M. H. Albert, M. D. Atkinson and Robert Brignall, The enumeration of three pattern classes, arXiv:1206.3183 [math.CO], (2012), p. 14 (Lemma 4.3).

Index entries for linear recurrences with constant coefficients, signature (3,0,-4).

Formula

G.f.: x^4*(2-3*x-x^2)/((1+x)*(1-2*x)^2).

a(n) = (2^(n-5)*(3*n+16)+4*(-1)^n)/9 with n>3, a(0)=a(1)=a(2)=a(3)=0. [Bruno Berselli, Nov 29 2012]

Mathematica

CoefficientList[Series[x^4 (2 - 3 x - x^2)/((1 + x) (1 - 2 x)^2), {x, 0, 35}], x] (* Bruno Berselli, Nov 30 2012 *)

Prog

(Maxima) makelist(coeff(taylor(x^4*(2-3*x-x^2)/((1+x)*(1-2*x)^2), x, 0, n), x, n), n, 0, 35); /* Bruno Berselli, Nov 29 2012 */
(Magma) I:=[0, 0, 0, 0, 2, 3, 8]; [n le 7 select I[n] else 3*Self(n-1) - 4*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Dec 14 2012

Crossrefs

Cf. A219752-A219759, A219837.

Sequence in context: A261984 A100321 A324839 * A121133 A011952 A032104

Adjacent sequences: A219748 A219749 A219750 * A219752 A219753 A219754

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 28 2012

Status

approved