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A266354
Expansion of b(2)*b(6)*b(10)/(1 - x - x^2 - x^4 - x^5 + x^11 + x^12 + x^14), where b(k) = (1-x^k)/(1-x).
2
1, 4, 10, 21, 41, 78, 145, 266, 485, 882, 1601, 2902, 5256, 9516, 17226, 31180, 56435, 102143, 184868, 334588, 605559, 1095976, 1983558, 3589950, 6497282, 11759123, 21282277, 38517777, 69711482, 126167473, 228344464, 413269701, 747957021, 1353691555, 2449981446
OFFSET
0,2
COMMENTS
This is the Poincaré series [or Poincare series] for the quasi-Lannér diagram QL4_19 - see Table 7.8 in Maxim Chapovalov, Dimitry Leites and Rafael Stekolshchik (2009), or equivalently Table 6 in the shorter version, Maxim Chapovalov, Dimitry Leites and Rafael Stekolshchik (2010).
LINKS
Maxim Chapovalov, Dimitry Leites, and Rafael Stekolshchik, The Poincaré series [or Poincare series] of the hyperbolic Coxeter groups with finite volume of fundamental domains, arXiv:0906.1596 [math.RT], 2009, page 31.
Maxim Chapovalov, Dimitry Leites, and Rafael Stekolshchik, The Poincaré series [or Poincare series] of the hyperbolic Coxeter groups with finite volume of fundamental domains, Journal of Nonlinear Mathematical Physics, Volume 17, Supplement 1 (2010), page 186.
FORMULA
G.f.: (1 + x)^3*(1 - x + x^2)*(1 + x + x^2)*(1 - x + x^2 - x^3 + x^4)/((1 - x)*(1 - x - x^2 - x^4 - x^6 - x^7 - x^9)).
MATHEMATICA
CoefficientList[Series[(1 + x)^3 (1 - x + x^2) (1 + x + x^2) (1 - x + x^2 - x^3 + x^4)/((1 - x) (1 - x - x^2 - x^4 - x^6 - x^7 - x^9)), {x, 0, 40}], x]
PROG
(Magma) /* By definition: */ m:=40; R<x>:=PowerSeriesRing(Integers(), m); b:=func<k|(1-x^k)/(1-x)>; Coefficients(R!(b(2)*b(6)*b(10)/(1-x-x^2-x^4-x^5+x^11+x^12+x^14)));
CROSSREFS
Cf. similar sequences listed in A265055.
Sequence in context: A265053 A266371 A293823 * A121497 A132925 A264079
KEYWORD
nonn,easy
AUTHOR
Bruno Berselli, Dec 28 2015
STATUS
approved