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A051630 Poincaré series [or Poincare series] (or Molien series) for Gamma_2(1,2)_(2). 1
1, 0, 2, 2, 4, 5, 9, 9, 15, 17, 23, 27, 36, 39, 51, 57, 69, 78, 94, 102, 122, 134, 154, 170, 195, 210, 240, 260, 290, 315, 351, 375, 417, 447, 489, 525, 574, 609, 665, 707, 763, 812, 876, 924, 996, 1052, 1124, 1188, 1269, 1332, 1422, 1494, 1584 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
B. Runge, Codes and Siegel modular forms, Discrete Math. 148 (1996), 175-204, p. 202, last displayed formula.
Index entries for linear recurrences with constant coefficients, signature (1,1,0,-1,-1,2,-1,-1,0,1,1,-1).
FORMULA
a(n) ~ (1/108)*n^3 + (1/18)*n^2. - Ralf Stephan, Apr 29 2014
G.f.: ( 1+x^2-x+x^4 ) / ( (x^2-x+1)*(1+x)^2*(1+x+x^2)^2*(x-1)^4 ). - R. J. Mathar, Dec 18 2014
From Luce ETIENNE, Aug 14 2019: (Start)
a(n) = 4*a(n-6) - 6*a(n-12) + 4*a(n-18) - a(n-24).
a(n) = a(n-1) + a(n-2) - a(n-4) - a(n-5) + 2*a(n-6) - a(n-7) - a(n-8) + a(n-10) + a(n-11) - a(n-12).
a(n) = (240*floor(n/6)^3 + 60*(2*m+7)*floor(n/6)^2 - (16*m^5 - 205*m^4 + 930*m^3 - 1775*m^2 + 1034*m - 300)*floor(n/6) - 16*m^5 + 205*m^4 - 930*m^3 + 1775*m^2 - 1154*m + 120)/120 where m = n mod 6. (End)
MAPLE
(1 + x^3 + x^4 + x^5)/((1 - x^2)^2*(1 - x^3)*(1 - x^6));
MATHEMATICA
CoefficientList[ Series[ (1-x+x^2+x^4) / (1-x-x^2+x^4+x^5-2x^6+x^7+x^8-x^10-x^11+x^12), {x, 0, 52}], x] (* Jean-François Alcover, Dec 02 2011 *)
LinearRecurrence[{1, 1, 0, -1, -1, 2, -1, -1, 0, 1, 1, -1}, {1, 0, 2, 2, 4, 5, 9, 9, 15, 17, 23, 27}, 60] (* Harvey P. Dale, Dec 27 2016 *)
CROSSREFS
Sequence in context: A059850 A308906 A337823 * A050045 A308955 A098386
KEYWORD
nonn,nice,easy
AUTHOR
STATUS
approved

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Last modified March 28 16:58 EDT 2024. Contains 371254 sequences. (Running on oeis4.)