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A129443 Expansion of (-1+4*x^2+8*x^3)/((1 +2*x +4*x^2)*(-1 +x +2*x +4*x^2 +4*x^3 -16*x^4)). 1
1, 1, 3, 25, 75, 289, 1283, 4905, 19547, 79281, 315123, 1260153, 5049419, 20180865, 80722531, 322959049, 1291700027, 5166801489, 20667742419, 82669888537, 330679592235, 1322722573857, 5290881765955, 21163527357033, 84654142731803 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The generating function is the case q=2 of  (-1 + q^2*x^2 + q^3*x^3)/((1 + q*x + q^2*x^2)*(-1 + x + q*x + q^2*x^2 + q^2*x^3 - q^4*x^4)) in the Billey-Warrington paper.

[Note that this is actually not the g.f. in the paper which has an additional term q*x^2 in the second factor in the denominator - R. J. Mathar, Sep 09 2011]

LINKS

Table of n, a(n) for n=0..24.

Sara Billey, Gregory Warrington, Kazhdan-Lusztig Polynomials for 321-hexagon-avoiding permutations, J. of Algebraic Combinatorics 13 (2) (2001) 111-136, page 132.

FORMULA

G.f. (1-4*x^2-8*x^3)/ ( (1+2*x+4*x^2)*(4*x-1)*(4*x^3-x-1)).

MAPLE

(-1+4*x^2+8*x^3)/((1+2*x+4*x^2)*(-1+x+2*x+4*x^2+4*x^3-16*x^4)) ;

taylor(%, x=0, 10) ; # R. J. Mathar, Sep 09 2011

MATHEMATICA

p[x_, q_] = (-1 + q^2*x^2 + q^3*x^3)/((1 + q*x + q^2*x^2)*(-1 + x + q*x + q^2*x^2 + q^2*x^3 - q^4*x^4)); Table[ SeriesCoefficient[Series[p[x, 2], {x, 0, 30}], n], {n, 0, 30}]

PROG

(PARI) Vec((-1+4*x^2+8*x^3)/((1+2*x+4*x^2)*(-1+x+2*x+4*x^2+4*x^3-16*x^4))+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012

CROSSREFS

Sequence in context: A242974 A006222 A290165 * A083298 A083222 A041565

Adjacent sequences:  A129440 A129441 A129442 * A129444 A129445 A129446

KEYWORD

nonn,easy,less

AUTHOR

Roger L. Bagula, Jun 08 2007

STATUS

approved

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Last modified September 23 20:42 EDT 2021. Contains 347617 sequences. (Running on oeis4.)