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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).
2
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
OFFSET
0,4
LINKS
M. Baake, J. Hermisson, P. Pleasants, The torus parametrization of quasiperiodic LI-classes, J. Phys. A 30 (1997), no. 9, 3029-3056. See (31).
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 *)
LinearRecurrence[{1, 6, -1, -10, -1, 6, 1, -1}, {1, 1, 1, 6, 12, 36, 91, 241, 632}, 30] (* Harvey P. Dale, Sep 06 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: A352621 A176681 A064476 * A239171 A264955 A038266
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Mar 12 2019
STATUS
approved