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A324483 Expansion of (1-x-x^2)^2*(1+x-x^2)^2/((1-3*x+x^2)*(1-x)^2*(1+x)^4). 1
1, 1, 1, 6, 12, 36, 91, 241, 632, 1651, 4333, 11328, 29684, 77678, 203415, 532483, 1394144, 3649813, 9555465, 25016378, 65493916, 171465080, 448901667, 1175239525, 3076817368, 8055212055, 21088819397, 55211245460, 144544917748 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

M. Baake, J. Hermisson, P. Pleasants, The torus parametrization of quasiperiodic LI-classes, J. Phys. A 30 (1997), no. 9, 3029-3056. See (31).

Index entries for linear recurrences with constant coefficients, signature (1,6,-1,-10,-1,6,1,-1).

FORMULA

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

From Colin Barker, Mar 13 2019: (Start)

a(n) = 2^(-4-n)*(-768*sqrt(5)*((3-sqrt(5))^n - (3+sqrt(5))^n) - 5*(517*(-2)^n + 75*2^n)*n + 25*(-1)^n*2^(1+n)*n^3) / 375 for n>1.

a(n) = a(n-1) + 6*a(n-2) - a(n-3) - 10*a(n-4) - a(n-5) + 6*a(n-6) + a(n-7) - a(n-8) for n>8.

(End)

MATHEMATICA

CoefficientList[Series[(1 - x - x^2)^2 (1 + x - x^2)^2 / ((1 - 3 x + x^2) (1 - x)^2 (1 + x)^4), {x, 0, 33}], x] (* Vincenzo Librandi, Mar 13 2019 *)

PROG

(MAGMA) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1-x-x^2)^2*(1+x-x^2)^2/((1-3*x+x^2)*(1-x)^2*(1+x)^4)); // Vincenzo Librandi, Mar 13 2019

(PARI) Vec((1 + x - x^2)^2*(1 - x - x^2)^2 / ((1 - x)^2*(1 + x)^4*(1 - 3*x + x^2)) + O(x^30)) \\ Colin Barker, Mar 13 2019

CROSSREFS

Sequence in context: A212976 A176681 A064476 * A239171 A264955 A038266

Adjacent sequences:  A324480 A324481 A324482 * A324484 A324485 A324486

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Mar 12 2019

STATUS

approved

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Last modified August 18 04:50 EDT 2019. Contains 326072 sequences. (Running on oeis4.)