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

1, 1, 26, 51, 701, 1976, 19501, 68901, 556426, 2278951, 16189601, 73163376, 477903401, 2306987801, 14254572826, 71929267851, 428293588501, 2226525284776, 12933864997301, 68596997116701, 391943622049226

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Index entries for linear recurrences with constant coefficients, signature (1,25).

Formula

a(0)=1, a(1)=1, a(n) = a(n-1) + 25*a(n-2) for n>1. - Philippe Deléham, Sep 19 2009

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

Mathematica

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}]
Join[{a=1, b=1}, Table[c=1*b+25*a; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2011 *)
CoefficientList[Series[1/(1-x-25x^2), {x, 0, 30}], x] (* or *) LinearRecurrence[ {1, 25}, {1, 1}, 30] (* Harvey P. Dale, Dec 23 2014 *)

Prog

(C++)
// generates 9 terms in the sequence A122999 in OEIS
#include <iostream>
#include <cstdlib>
#include <cmath>
#include <iomanip>
using namespace std;
int main(int argc, char *argv[])
{
    for (int i=1; i < 10; i++)
    { 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);
    std::cout << i << ' ' << j << endl; }
return EXIT_SUCCESS;
}   // Antonio Alberto Olivares, Jun 06 2011
(Maxima) makelist(coeff(taylor(1/(1-x-25*x^2), x, 0, n), x, n), n, 0, 20); /* Bruno Berselli, Jun 06 2011 */
(PARI) Vec(O(x^99)+(1-x-25*x^2)^-1) \\ Charles R Greathouse IV, Jun 06, 2011

Crossrefs

Cf. A026597.

Sequence in context: A169861 A249912 A267039 * A040650 A252994 A288162

Adjacent sequences: A122996 A122997 A122998 * A123000 A123001 A123002

Keyword

nonn,easy

Author

Roger L. Bagula, Sep 22 2006

Extensions

Edited by N. J. A. Sloane, Sep 26 2006

Definition corrected by R. J. Mathar, Jan 15 2009

Status

approved