A112522 Expansion of (1+3*x+14*x^2-10*x^3-10*x^4+16*x^5+15*x^6-15*x^7-2*x^8+4*x^9+8*x^10) / ((1+4*x^2)*(1-x^2+x^4)*(1+x^2)^2).

1, 3, 9, -25, -59, 129, 273, -563, -1145, 2313, 4651, -9329, -18689, 37411, 74857, -149753, -299547, 599137, 1198321, -2396691, -4793433, 9586921, 19173899, -38347857, -76695777, 153391619, 306783305, -613566681, -1227133435, 2454266945, 4908533969, -9817068019, -19634136121

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,-5,0,-4,0,-1,0,-5,0,-4).

Formula

a(n) = -5*a(n-2) - 4*a(n-4) - a(n-6) - 5*a(n-8) - 4*a(n-10) for n > 10. - Colin Barker, May 18 2019

Mathematica

LinearRecurrence[{0, -5, 0, -4, 0, -1, 0, -5, 0, -4}, {1, 3, 9, -25, -59, 129, 273, -563, -1145, 2313, 4651}, 40] (* G. C. Greubel, Jan 12 2022 *)

Prog

(PARI) Vec((1+3*x+14*x^2-10*x^3-10*x^4+16*x^5+15*x^6-15*x^7-2*x^8+4*x^9+8*x^10)/( (1+4*x^2)*(1-x^2+x^4)*(1+x^2)^2)+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012
(Sage)
def A112522_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1 +3*x +14*x^2 -10*x^3 -10*x^4 +16*x^5 +15*x^6 -15*x^7 -2*x^8 +4*x^9 +8*x^10)/((1+4*x^2)*(1-x^2+x^4)*(1+x^2)^2) ).list()
A112522_list(40) # G. C. Greubel, Jan 12 2022
(Magma)
R<x>:=PowerSeriesRing(Rationals(), 40);
Coefficients(R!( (1 +3*x +14*x^2 -10*x^3 -10*x^4 +16*x^5 +15*x^6 -15*x^7 -2*x^8 +4*x^9 +8*x^10)/((1+4*x^2)*(1-x^2+x^4)*(1+x^2)^2) )); // G. C. Greubel, Jan 12 2022

Crossrefs

Cf. A112523.

Sequence in context: A032681 A293852 A005209 * A005262 A101357 A004255

Adjacent sequences: A112519 A112520 A112521 * A112523 A112524 A112525

Keyword

sign,easy

Author

Creighton Dement, Sep 09 2005

Status

approved