A219755 Expansion of x^4*(1-3*x^2-x^3)/((1+x)*(1-2*x)*(1-x-2*x^2)).

0, 0, 0, 0, 1, 2, 4, 9, 18, 39, 80, 169, 350, 731, 1516, 3149, 6522, 13503, 27912, 57649, 118934, 245155, 504868, 1038869, 2135986, 4388487, 9009984, 18486009, 37904078, 77672299, 159072860, 325602269, 666117610, 1362061391, 2783775096, 5686854849, 11612318982

Offset

0,6

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. 17 (Lemma 4.6).

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

Formula

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

a(n) = (2^(n-5)*(3*n+38)-(3*n-14)*(-1)^n)/27 with n>3, a(0)=a(1)=a(2)=a(3)=0. [Bruno Berselli, Nov 29 2012]

Mathematica

CoefficientList[Series[x^4 (1 - 3 x^2 - x^3)/((1 + x) (1 - 2 x) (1 - x - 2 x^2)), {x, 0, 36}], x] (* Bruno Berselli, Nov 30 2012 *)

Prog

(Maxima) makelist(coeff(taylor(x^4*(1-3*x^2-x^3)/((1+x)*(1-2*x)*(1-x-2*x^2)), x, 0, n), x, n), n, 0, 36); /* Bruno Berselli, Nov 29 2012 */
(Magma) I:=[0, 0, 0, 0, 1, 2, 4, 9]; [n le 8 select I[n] else 2*Self(n-1) + 3*Self(n-2) - 4*Self(n-3) - 4*Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 15 2012

Crossrefs

Cf. A219751-A219759, A219837.

Sequence in context: A329668 A320222 A036610 * A289846 A193201 A038044

Adjacent sequences: A219752 A219753 A219754 * A219756 A219757 A219758

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 28 2012

Status

approved