OFFSET
1,2
COMMENTS
The sequence can also be generated by adding of the top-row elements of the (n-1)st power of the matrix [[0,1],[1,1/5]] and multiplying with 5^(n-1).
LINKS
Nathaniel Johnston, Table of n, a(n) for n = 1..500
Index entries for linear recurrences with constant coefficients, signature (1,25)
FORMULA
a(n) = a(n-1)+25*a(n-2). [Philippe Deléham, Mar 26 2009]
a(n) = (1/2+9*sqrt(101)/202)*(1/2+sqrt(101)/2)^(n-1) + (1/2-9*sqrt(101)/202)*(1/2-sqrt(101)/2)^(n-1). [Antonio Alberto Olivares, Jun 07 2011]
MATHEMATICA
M := {{0, 1}, {1, 1/5}}; v[1] = {1, 1}; v[n_] := v[n] = M.v[n - 1]; a = Table[v[n][[1]]*5^(n - 1), {n, 1, 30}]
LinearRecurrence[{1, 25}, {1, 5}, 30] (* Harvey P. Dale, Mar 11 2017 *)
PROG
(PARI) Vec(x*(1+4*x)/(1-x-25*x^2) + O(x^30)) \\ Michel Marcus, Jan 28 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, Sep 22 2006
EXTENSIONS
Replaced definition by a specific one - The Assoc. Eds. of the OEIS, Jun 07 2010
More terms from Michel Marcus, Jan 28 2015
STATUS
approved