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A176288 Hankel transform of A176287. 2
1, 3, 15, 55, 131, 163, -169, -1521, -4437, -7429, -2945, 26471, 101587, 207699, 201639, -306497, -1907461, -4718165, -6464305, 547863, 30463779, 93816323, 161591287, 97035119, -400669877, -1676486565, -3504149217, -3693262649 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,-17,24,-16).

FORMULA

G.f.: (1-3*x+14*x^2-8*x^3)/(1-3*x+4*x^2)^2.

a(n) = 2^n*( (2n+7)*sin(2n*atan(1/sqrt(7)))/sqrt(7) - (2*n-1)*cos(2n*atan(1/sqrt(7)))).

MAPLE

seq(coeff(series((1-3*x+14*x^2-8*x^3)/(1-3*x+4*x^2)^2, x, n+1), x, n), n = 0..30); # G. C. Greubel, Nov 25 2019

MATHEMATICA

LinearRecurrence[{6, -17, 24, -16}, {1, 3, 15, 55}, 30] (* Harvey P. Dale, Jun 12 2017 *)

PROG

(PARI) my(x='x+O('x^30)); Vec((1-3*x+14*x^2-8*x^3)/(1-3*x+4*x^2)^2) \\ G. C. Greubel, Nov 25 2019

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1-3*x+14*x^2-8*x^3)/(1-3*x+4*x^2)^2 )); // G. C. Greubel, Nov 25 2019

(Sage)

def A176288_list(prec):

    P.<x> = PowerSeriesRing(ZZ, prec)

    return P( (1-3*x+14*x^2-8*x^3)/(1-3*x+4*x^2)^2 ).list()

A176288_list(30) # G. C. Greubel, Nov 25 2019

(GAP) a:=[1, 3, 15, 55];; for n in [5..30] do a[n]:=6*a[n-1]-17*a[n-2]+24*a[n-3] -16*a[n-4]; od; a; # G. C. Greubel, Nov 25 2019

CROSSREFS

Sequence in context: A082708 A093925 A117960 * A119113 A286185 A152896

Adjacent sequences:  A176285 A176286 A176287 * A176289 A176290 A176291

KEYWORD

easy,sign

AUTHOR

Paul Barry, Apr 14 2010

STATUS

approved

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Last modified August 10 19:52 EDT 2020. Contains 336381 sequences. (Running on oeis4.)