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A266367
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Expansion of b(2)*b(4)/(1 - 2*x - 2*x^3 + 3*x^4), where b(k) = (1-x^k)/(1-x).
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2
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1, 4, 10, 24, 54, 116, 250, 536, 1142, 2436, 5194, 11064, 23574, 50228, 107002, 227960, 485654, 1034628, 2204170, 4695768, 10003830, 21312116, 45403258, 96726872, 206066486, 439003140, 935250250, 1992452856, 4244712534, 9042916148, 19264987258, 41042041016, 87435776726
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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_16 - 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)^2*(1 + x^2)/((1 - x)*(1 - x - x^2 - 3*x^3)).
a(n) = 2*a(n-1) + 2*a(n-3) - 3*a(n-4) for n>4.
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MATHEMATICA
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CoefficientList[Series[(1 + x)^2 (1 + x^2)/((1 - x) (1 - x - x^2 - 3 x^3)), {x, 0, 40}], x]
LinearRecurrence[{2, 0, 2, -3}, {1, 4, 10, 24, 54}, 40] (* Harvey P. Dale, Mar 22 2016 *)
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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(2)*b(4)/(1-2*x-2*x^3+3*x^4)));
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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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