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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

Vincenzo Librandi, Table of n, a(n) for n = 0..800

Index entries for linear recurrences with constant coefficients, signature (18,-1).

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: A156455 A089350 A323961 * A053508 A060918 A115100

Adjacent sequences:  A004289 A004290 A004291 * A004293 A004294 A004295

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified August 22 11:34 EDT 2019. Contains 326176 sequences. (Running on oeis4.)