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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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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):
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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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CROSSREFS
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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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