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A266336
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G.f. = b(2)*b(6)/(x^6-x^4+x^2-2*x+1), where b(k) = (1-x^k)/(1-x).
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2
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1, 4, 9, 16, 26, 42, 67, 104, 158, 238, 359, 542, 816, 1224, 1833, 2746, 4116, 6168, 9237, 13828, 20702, 30998, 46415, 69492, 104034, 155746, 233171, 349090, 522628, 782420, 1171349, 1753622, 2625352, 3930412, 5884193, 8809176, 13188162, 19743938, 29558555
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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_5 - see Tables 7.6, 7.7 and 7.8 in Maxim Chapovalov, Dimitry Leites and Rafael Stekolshchik (2009), or equivalently Tables 5 and 6 in the shorter version, Maxim Chapovalov, Dimitry Leites and Rafael Stekolshchik (2010).
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LINKS
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MAPLE
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gf:= b(2)*b(6)/(x^6-x^4+x^2-2*x+1):
b:= k->(1-x^k)/(1-x):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..40);
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MATHEMATICA
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b[k_] := (1 - x^k)/(1 - x); CoefficientList[Series[b[2] b[6]/(x^6 - x^4 + x^2 - 2 x + 1), {x, 0, 40}], x] (* Bruno Berselli, Dec 29 2015 *)
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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(6)/(x^6-x^4+x^2-2*x+1))); // Bruno Berselli, Dec 29 2015
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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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