A219752 Expansion of 2*x^4*(1-2*x+x^4)/((1+x)*(1-2*x)^2*(1-x-x^2)).

0, 0, 0, 0, 2, 4, 12, 26, 62, 136, 302, 654, 1412, 3018, 6422, 13592, 28662, 60230, 126212, 263810, 550222, 1145352, 2380062, 4938078, 10230852, 21169114, 43749862, 90317816, 186263462, 383769046, 790000452, 1624890194, 3339501662, 6858353128, 14075255822

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. 17 (Lemma 4.4).

Index entries for linear recurrences with constant coefficients, signature (4,-2,-7,4,4).

Formula

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

a(n) = 2*A219753(n). - Bruno Berselli, Nov 29 2012

Mathematica

CoefficientList[Series[2 x^4 (1 - 2 x + x^4)/((1 + x) (1 - 2 x)^2 (1 - x - x^2)), {x, 0, 34}], x] (* Bruno Berselli, Nov 30 2012 *)
LinearRecurrence[{4, -2, -7, 4, 4}, {0, 0, 0, 0, 2, 4, 12, 26, 62}, 40] (* Harvey P. Dale, Mar 09 2023 *)

Prog

(Maxima) makelist(coeff(taylor(2*x^4*(1-2*x+x^4)/((1+x)*(1-2*x)^2*(1-x-x^2)), x, 0, n), x, n), n, 0, 34); /* Bruno Berselli, Nov 29 2012 */
(Magma) I:=[0, 0, 0, 0, 2, 4, 12, 26, 62]; [n le 9 select I[n] else 4*Self(n-1) - 2*Self(n-2) - 7*Self(n-3) + 4*Self(n-4) + 4*Self(n-5): n in [1..40]]; // Vincenzo Librandi, Dec 14 2012

Crossrefs

Cf. A219751-A219759, A219837.

Sequence in context: A045678 A236002 A291406 * A242536 A027132 A148172

Adjacent sequences: A219749 A219750 A219751 * A219753 A219754 A219755

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 28 2012

Status

approved