A199629 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=3.

1, 6, 16, 35, 86, 182, 317, 558, 975, 1514, 2249, 3366, 4749, 6338, 8417, 10920, 13563, 16538, 19961, 23514, 27123, 30974, 34997, 38994, 42972, 47048, 51197, 55285, 59313, 63408, 67567, 71660, 75689, 79784, 83943, 88036, 92065, 96160, 100319, 104412, 108441, 112536, 116695, 120788, 124817, 128912

Offset

0,2

Comments

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

Links

Colin Barker, 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

From Colin Barker, Nov 05 2019: (Start)

G.f.: (x^31 + 4*x^30 + 6*x^29 + 13*x^28 + 37*x^27 + 54*x^26 + 72*x^25 + 153*x^24 + 216*x^23 + 228*x^22 + 372*x^21 + 504*x^20 + 462*x^19 + 588*x^18 + 756*x^17 + 630*x^16 + 630*x^15 + 756*x^14 + 588*x^13 + 462*x^12 + 504*x^11 + 372*x^10 + 228*x^9 + 215*x^8 + 151*x^7 + 71*x^6 + 54*x^5 + 37*x^4 + 13*x^3 + 6*x^2 + 4*x + 1) / (x^4 - 2*x^3 + 2*x^2 - 2*x + 1).

a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - a(n-4) for n>31.

(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(3);

Prog

(Magma) g:=3; m:=46; 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((x^31 + 4*x^30 + 6*x^29 + 13*x^28 + 37*x^27 + 54*x^26 + 72*x^25 + 153*x^24 + 216*x^23 + 228*x^22 + 372*x^21 + 504*x^20 + 462*x^19 + 588*x^18 + 756*x^17 + 630*x^16 + 630*x^15 + 756*x^14 + 588*x^13 + 462*x^12 + 504*x^11 + 372*x^10 + 228*x^9 + 215*x^8 + 151*x^7 + 71*x^6 + 54*x^5 + 37*x^4 + 13*x^3 + 6*x^2 + 4*x + 1) / (x^4 - 2*x^3 + 2*x^2 - 2*x + 1) + O(x^70)) \\ Colin Barker, Nov 05 2019

Crossrefs

Sequence in context: A192749 A160997 A334047 * A098943 A321973 A178465

Adjacent sequences: A199626 A199627 A199628 * A199630 A199631 A199632

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 08 2011

Status

approved