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A004292 Expansion of (1+x)^2/(1-18*x+x^2). 2
1, 20, 360, 6460, 115920, 2080100, 37325880, 669785740, 12018817440, 215668928180, 3870021889800, 69444725088220, 1246135029698160, 22360985809478660, 401251609540917720, 7200167985927040300 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
REFERENCES
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.
LINKS
Hacène Belbachir, Soumeya Merwa Tebtoub, László Németh, Ellipse Chains and Associated Sequences, J. Int. Seq., Vol. 23 (2020), Article 20.8.5.
FORMULA
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
MAPLE
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
MATHEMATICA
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 *)
PROG
(PARI) Vec((1+x)^2/(1-18*x+x^2)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
CROSSREFS
Pairwise sums of A049629.
Sequence in context: A358365 A089350 A323961 * A053508 A060918 A115100
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)