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A004292
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Expansion of (1+x)^2/(1-18*x+x^2).
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2
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1, 20, 360, 6460, 115920, 2080100, 37325880, 669785740, 12018817440, 215668928180, 3870021889800, 69444725088220, 1246135029698160, 22360985809478660, 401251609540917720, 7200167985927040300
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OFFSET
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0,2
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REFERENCES
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J. M. Alonso, Growth functions of amalgams, in Alperin, ed., Arboreal Group Theory, Springer, pp. 1-34, esp. p. 32.
P. de la Harpe, Topics in Geometric Group Theory, Univ. Chicago Press, 2000, p. 160, middle display.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..800
Hacène Belbachir, Soumeya Merwa Tebtoub, László Németh, Ellipse Chains and Associated Sequences, J. Int. Seq., Vol. 23 (2020), Article 20.8.5.
Index entries for linear recurrences with constant coefficients, signature (18,-1).
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FORMULA
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a(n) = 1/2*(1-(-1)^2^n+(20+9*sqrt(5))*((9+4*sqrt(5))^(2*n)-1)/(9+4*sqrt(5))^(n+1)). - Gerry Martens, May 30 2015
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MAPLE
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f:= gfun:-rectoproc({a(n)=18*a(n-1)-a(n-2), a(0)=1, a(1)=20, a(2)=360}, a(n), remember):
map(f, [$0..20]); # Robert Israel, Jun 01 2015
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MATHEMATICA
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CoefficientList[Series[(1+x)^2/(1-18*x+x^2), {x, 0, 20}], x] (* Vincenzo Librandi, Jun 13 2012 *)
a[n_]:=1/2(1-(-1)^2^n+(20+9 Sqrt[5])((9+4 Sqrt[5])^(2 n)-1)/(9+4 Sqrt[5])^(n+1)); Table[a[n] // FullSimplify, {n, 0, 20}] (* Gerry Martens, May 30 2015 *)
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PROG
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(PARI) Vec((1+x)^2/(1-18*x+x^2)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
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CROSSREFS
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Pairwise sums of A049629.
Sequence in context: A156455 A089350 A323961 * A053508 A060918 A115100
Adjacent sequences: A004289 A004290 A004291 * A004293 A004294 A004295
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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