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A122999
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G.f.: 1/(1-x-25*x^2).
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3
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1, 1, 26, 51, 701, 1976, 19501, 68901, 556426, 2278951, 16189601, 73163376, 477903401, 2306987801, 14254572826, 71929267851, 428293588501, 2226525284776, 12933864997301, 68596997116701, 391943622049226
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (1,25).
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FORMULA
| a(0)=1, a(1)=1, a(n)=a(n-1)+25*a(n-2) for n>1. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 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) [From Antonio Alberto Olivares (olivares14031(AT)yahoo.com), Jun 06 2011]
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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}]] (*From Vladimir Joseph Stephan Orlovsky, Feb 01 2011*)
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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, olivares14031(AT)yahoo.com, 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
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CROSSREFS
| Cf. A026597.
Sequence in context: A044459 A158060 A169861 * A040650 A121738 A043331
Adjacent sequences: A122996 A122997 A122998 * A123000 A123001 A123002
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KEYWORD
| nonn,easy
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AUTHOR
| Roger Bagula (rlbagulatftn(AT)yahoo.com), Sep 22 2006
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Sep 26 2006
Corrected definition R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 15 2009
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