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A266337
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Expansion of b(3)*b(4)/(1 - 2*x + x^5), where b(k) = (1-x^k)/(1-x).
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2
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1, 4, 11, 25, 52, 104, 204, 397, 769, 1486, 2868, 5532, 10667, 20565, 39644, 76420, 147308, 283949, 547333, 1055022, 2033624, 3919940, 7555931, 14564529, 28074036, 54114448, 104308956, 201061981, 387559433, 747044830, 1439975212, 2775641468
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OFFSET
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0,2
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COMMENTS
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This is the Poincaré series [or Poincare series] for the quasi-Lannér diagram QL4_21 - 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).
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LINKS
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FORMULA
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G.f.: (1 + x)*(1 + x^2)*(1 + x + x^2)/((1 - x)*(1 - x - x^2 - x^3 - x^4)).
a(n) = 2*a(n-1) - a(n-5) for n>5.
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MATHEMATICA
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CoefficientList[Series[(1 + x) (1 + x^2) (1 + x + x^2)/((1 - x) (1 - x - x^2 - x^3 - x^4)), {x, 0, 40}], x]
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PROG
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(Magma) /* By definition: */ m:=40; R<x>:=PowerSeriesRing(Integers(), m); b:=func<k|(1-x^k)/(1-x)>; Coefficients(R!(b(3)*b(4)/(1-2*x+x^5)));
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CROSSREFS
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Cf. similar sequences listed in A265055.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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