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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
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listen;
history;
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OFFSET
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0,3
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LINKS
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FORMULA
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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
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MATHEMATICA
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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}]
CoefficientList[Series[1/(1-x-25x^2), {x, 0, 30}], x] (* or *) LinearRecurrence[ {1, 25}, {1, 1}, 30] (* Harvey P. Dale, Dec 23 2014 *)
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PROG
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(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;
(Maxima) makelist(coeff(taylor(1/(1-x-25*x^2), x, 0, n), x, n), n, 0, 20); /* Bruno Berselli, Jun 06 2011 */
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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