cp's OEIS Frontend

A122999 G.f.: 1/(1 - x - 25*x^2).

%I A122999 #36 Jun 29 2025 21:25:25
%S A122999 1,1,26,51,701,1976,19501,68901,556426,2278951,16189601,73163376,
%T A122999 477903401,2306987801,14254572826,71929267851,428293588501,
%U A122999 2226525284776,12933864997301,68596997116701,391943622049226
%N A122999 G.f.: 1/(1 - x - 25*x^2).
%H A122999 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,25).
%F A122999 a(0)=1, a(1)=1, a(n) = a(n-1) + 25*a(n-2) for n>1. - _Philippe Deléham_, Sep 19 2009
%F A122999 a(n) = (1/2 + sqrt(101)/202)*(1/2 + sqrt(101)/2)^(n-1) + (1/2 - sqrt(101)/202)*(1/2 - sqrt(101)/2)^(n-1). - _Antonio Alberto Olivares_, Jun 06 2011
%t A122999 m =5; p[x_] := -1 - x/m + x^2; q[x_] := ExpandAll[x^2*p[1/x]]; Table[ SeriesCoefficient[Series[x/q[x], {x, 0, 30}], n]*m^(n - 1), {n, 0, 30}]
%t A122999 Join[{a=1,b=1},Table[c=1*b+25*a;a=b;b=c,{n,60}]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 01 2011 *)
%t A122999 CoefficientList[Series[1/(1-x-25x^2),{x,0,30}],x] (* or *) LinearRecurrence[ {1,25},{1,1},30] (* _Harvey P. Dale_, Dec 23 2014 *)
%o A122999 (C++)
%o A122999 // generates 9 terms in the sequence A122999 in OEIS
%o A122999 #include <iostream>
%o A122999 #include <cstdlib>
%o A122999 #include <cmath>
%o A122999 #include <iomanip>
%o A122999 using namespace std;
%o A122999 int main(int argc, char *argv[])
%o A122999 {
%o A122999     for (int i=1; i < 10; i++)
%o A122999     { double j; j = (1.0/2.0+sqrt(101)/202.0)*pow((1.0/2.0+sqrt(101.0)/2.0), i-1)+(1.0/2.0-sqrt(101)/202.0)*pow((1.0/2.0-sqrt(101.0)/2.0), i-1);
%o A122999     std::cout << i << ' ' << j << endl; }
%o A122999 return EXIT_SUCCESS;
%o A122999 }   // _Antonio Alberto Olivares_, Jun 06 2011
%o A122999 (Maxima) makelist(coeff(taylor(1/(1-x-25*x^2), x, 0, n), x, n), n, 0, 20); /* _Bruno Berselli_, Jun 06 2011 */
%o A122999 (PARI) Vec(O(x^99)+(1-x-25*x^2)^-1) \\ _Charles R Greathouse IV_, Jun 06 2011
%Y A122999 Cf. A026597.
%K A122999 nonn,easy
%O A122999 0,3
%A A122999 _Roger L. Bagula_, Sep 22 2006
%E A122999 Edited by _N. J. A. Sloane_, Sep 26 2006
%E A122999 Definition corrected by _R. J. Mathar_, Jan 15 2009