A219754 Expansion of x^4*(1-x-x^2)/((1+x)*(1-2*x)*(1-x-2*x^2)).

0, 0, 0, 0, 1, 1, 4, 7, 18, 37, 84, 179, 390, 833, 1784, 3791, 8042, 16989, 35804, 75243, 157774, 330105, 689344, 1436935, 2990386, 6213781, 12893604, 26719267, 55302678, 114333617, 236123784, 487160639, 1004147450, 2067947213, 4255199084, 8749007451, 17975233502

Offset

0,7

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 4.5).

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

Formula

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

a(n) = (2^(n-4)*(3*n+5)+(3*n-2)*(-1)^n)/27 for n=1 and n>2, a(0)=a(1)=a(2)=0. [Bruno Berselli, Nov 29 2012]

Mathematica

CoefficientList[Series[x^4 (1 - x - x^2)/((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-x-x^2)/((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, 1, 4, 7]; [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: A146387 A219498 A358078 * A289975 A124400 A077920

Adjacent sequences: A219751 A219752 A219753 * A219755 A219756 A219757

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 28 2012

Status

approved