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A266353
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Expansion of b(3)*b(4)/(1 - 2*x + x^2 - x^3 + x^4), where b(k) = (1-x^k)/(1-x).
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2
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1, 4, 10, 20, 35, 57, 89, 136, 205, 306, 454, 671, 989, 1455, 2138, 3139, 4606, 6756, 9907, 14525, 21293, 31212, 45749, 67054, 98278, 144039, 211105, 309395, 453446, 664563, 973970, 1427428, 2092003, 3065985, 4493425, 6585440, 9651437, 14144874, 20730326, 30381775
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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_17 - 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^3)).
a(n) = 2*a(n-1) - a(n-2) + a(n-3) - a(n-4) for n>5.
a(n) = a(n-1) + a(n-3) + 12 for n>4. - Greg Dresden, Feb 09 2020
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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^3)), {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^2-x^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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