A219757 Expansion of x^4*(2-7*x+6*x^2+x^3-x^4)/((1-x)*(1-2*x)^4*(1-3*x+x^2)).

0, 0, 0, 0, 2, 17, 90, 383, 1436, 4958, 16159, 50480, 152690, 450343, 1301764, 3701990, 10387887, 28827688, 79265482, 216271927, 586261980, 1580524894, 4241295935, 11336890720, 30202962402, 80239307847, 212664541940, 562513804438, 1485379408591, 3916726647768

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. 25.

Index entries for linear recurrences with constant coefficients, signature (12,-60,161,-248,216,-96,16).

Formula

G.f.: x^4*(2-7*x+6*x^2+x^3-x^4)/((1-x)*(1-2*x)^4*(1-3*x+x^2)).

Mathematica

CoefficientList[Series[x^4(2-7x+6x^2+x^3-x^4)/((1-x)(1-2x)^4(1-3x+x^2)), {x, 0, 40}], x] (* Harvey P. Dale, Nov 29 2012 *)

Prog

(Maxima) makelist(coeff(taylor(x^4*(2-7*x+6*x^2+x^3-x^4)/((1-x)*(1-2*x)^4*(1-3*x+x^2)), x, 0, n), x, n), n, 0, 29); /* Bruno Berselli, Nov 29 2012 */
(Magma) I:=[0, 0, 0, 0, 2, 17, 90, 383, 1436, 4958]; [n le 10 select I[n] else 12*Self(n-1) - 60*Self(n-2) + 161*Self(n-3) - 248*Self(n-4) + 216*Self(n-5) - 96*Self(n-6) + 16*Self(n-7): n in [1..30]]; // Vincenzo Librandi, Dec 14 2012

Crossrefs

Cf. A219751-A219759, A219837.

Sequence in context: A320644 A081744 A372189 * A297727 A358591 A002645

Adjacent sequences: A219754 A219755 A219756 * A219758 A219759 A219760

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 28 2012

Status

approved