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A266335
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G.f. = b(2)^2*b(6)/(x^7+x^6-x^5-x^2-x+1), where b(k) = (1-x^k)/(1-x).
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2
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1, 4, 9, 17, 30, 52, 88, 145, 237, 386, 628, 1020, 1653, 2677, 4334, 7016, 11356, 18377, 29737, 48118, 77860, 125984, 203849, 329837, 533690, 863532, 1397228, 2260765, 3657997, 5918766, 9576768, 15495540, 25072313, 40567857, 65640174, 106208036, 171848216
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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_4 - 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)^2*b(6)/(x^7+x^6-x^5-x^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]^2 b[6]/(x^7 + x^6 - x^5 - x^2 - x + 1), {x, 0, 40}], x] (* Bruno Berselli, Dec 29 2015 *)
LinearRecurrence[{1, 1, 0, 0, 1, -1, -1}, {1, 4, 9, 17, 30, 52, 88, 145}, 40] (* Harvey P. Dale, Mar 23 2020 *)
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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)^2*b(6)/(x^7+x^6-x^5-x^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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