A199628 G.f.: (1+x)^(2*g)*(1+x^3)^(3*g)/((1-x^2)*(1-x^4))-x^(2*g)*(1+x)^4/((1-x^2)*(1-x^4)) for g=2.

1, 4, 7, 14, 32, 50, 71, 122, 185, 238, 319, 430, 528, 626, 752, 884, 1000, 1116, 1249, 1384, 1503, 1620, 1753, 1888, 2007, 2124, 2257, 2392, 2511, 2628, 2761, 2896, 3015, 3132, 3265, 3400, 3519, 3636, 3769, 3904, 4023, 4140, 4273, 4408, 4527, 4644, 4777, 4912, 5031, 5148, 5281, 5416, 5535, 5652, 5785, 5920, 6039, 6156, 6289, 6424

Offset

0,2

Comments

Expansion of a Poincaré series [or Poincare series] for space of moduli M_2 of stable bundles.

Links

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

Bott, Raoul, Lectures on Morse theory, old and new, Bull. Amer. Math. Soc. 7 (1982), no. 2, 331-358; reprinted in Vol. 48 (October, 2011). See Eq. (4.30).

Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1).

Formula

G.f.: (1+x)^4*(1+x^3)^6 / ((1-x^2)*(1-x^4))-x^4*(1+x)^4 / ((1-x^2)*(1-x^4)).

From Colin Barker, Nov 05 2019: (Start)

G.f.: (1 + x)^2*(1 - x^2 + 3*x^3 + 3*x^6 + x^9)*(1 + x^2 + 3*x^3 + 3*x^6 + x^9) / ((1 - x)^2*(1 + x^2)).

a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - a(n-4) for n>20.

(End)

Maple

f:=g->(1+x)^(2*g)*(1+x^3)^(3*g)/((1-x^2)*(1-x^4))-x^(2*g)*(1+x)^4/((1-x^2)*(1-x^4));
s:=g->seriestolist(series(f(g), x, 60));
s(2);

Mathematica

CoefficientList[Series[(1 + x)^4 (1 + x^3)^6 / ((1 - x^2) (1 - x^4)) - x^4 (1 + x)^4 / ((1 - x^2) (1 - x^4)), {x, 0, 33}], x] (* Vincenzo Librandi, Sep 07 2016 *)

Prog

(Magma) g:=2; m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+x)^(2*g)*(1+x^3)^(3*g)/((1-x^2)*(1-x^4))-x^(2*g)*(1+x)^4/((1-x^2)*(1-x^4))));  // Bruno Berselli, Nov 08 2011
(PARI) Vec((1 + x)^2*(1 - x^2 + 3*x^3 + 3*x^6 + x^9)*(1 + x^2 + 3*x^3 + 3*x^6 + x^9) / ((1 - x)^2*(1 + x^2)) + O(x^60)) \\ Colin Barker, Nov 05 2019

Crossrefs

Sequence in context: A076975 A050343 A245002 * A049945 A234576 A076586

Adjacent sequences: A199625 A199626 A199627 * A199629 A199630 A199631

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 08 2011

Status

approved