OFFSET
0,2
COMMENTS
Expansion of a Poincaré series [or Poincare series] for space of moduli M_2 of stable bundles.
LINKS
Georg Fischer, Table of n, a(n) for n = 0..999
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
a(n) = A047538(n-3) for n >= 6. - Georg Fischer, Oct 28 2018
From Colin Barker, Nov 05 2019: (Start)
G.f.: (1 + x)^2*(1 - 2*x + 2*x^2 - x^3 - x^4 + 3*x^5 - 2*x^6 + x^7) / ((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>9.
a(n) = (-16 + (-i)^(1+n) + i^(1+n) + 4*n) / 2 for n>5, where i=sqrt(-1).
(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(1);
PROG
(Magma) g:=1; 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 - 2*x + 2*x^2 - x^3 - x^4 + 3*x^5 - 2*x^6 + x^7) / ((1 - x)^2*(1 + x^2)) + O(x^70)) \\ Colin Barker, Nov 05 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 08 2011
STATUS
approved