login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Expansion of (1+2*x+x^2)/(1-50*x+x^2).
1

%I #20 Apr 16 2016 11:38:07

%S 1,52,2600,129948,6494800,324610052,16224007800,810875779948,

%T 40527564989600,2025567373700052,101237841120013000,

%U 5059866488626949948,252892086590227484400,12639544463022747270052,631724331064547136018200,31573577008764334053639948

%N Expansion of (1+2*x+x^2)/(1-50*x+x^2).

%D P. de la Harpe, Topics in Geometric Group Theory, Univ. Chicago Press, 2000, p. 160, middle display.

%H Vincenzo Librandi, <a href="/A004296/b004296.txt">Table of n, a(n) for n = 0..500</a>

%H J. M. Alonso, <a href="http://dx.doi.org/10.1007/978-1-4612-3142-4_1">Growth functions of amalgams</a>, in Alperin, ed., Arboreal Group Theory, Springer, pp. 1-34, esp. p. 32.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (50,-1).

%F From _Colin Barker_, Apr 16 2016: (Start)

%F a(n) = (sqrt(13/3)*(25+4*sqrt(39))^(-n)*(-1+(25+4*sqrt(39))^(2*n)))/2 for n>0.

%F a(n) = 50*a(n-1) - a(n-2) for n>2.

%F (End)

%F a(n) = (-3*(-1)^(2^n) + 2*sqrt(39)*sinh(n*log(25+4*sqrt(39))) + 3)/6. - _Ilya Gutkovskiy_, Apr 16 2016

%t CoefficientList[Series[(1+2*x+x^2)/(1-50*x+x^2),{x,0,30}],x] (* _Vincenzo Librandi_, Feb 25 2012 *)

%o (PARI) Vec((1+2*x+x^2)/(1-50*x+x^2)+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_