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

Author

Roger L. Bagula, Sep 22 2006

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A026597.

Programs

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 *)

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

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

Extensions

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

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