OFFSET
1,1
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,5).
FORMULA
a(n) = (2-(-1)^n)*5^(1/4*(2*n-1+(-1)^n)).
G.f.: x*(3+5*x)/(1-5*x^2).
a(n) = A056487(n), n>=1.
E.g.f.: cosh(sqrt(5)*x) + 3*sinh(sqrt(5)*x)/sqrt(5) - 1. - Stefano Spezia, Nov 19 2023
MATHEMATICA
CoefficientList[Series[x*(3 + 5*x)/(1 - 5*x^2), {x, 0, 50}], x] (* G. C. Greubel, Dec 21 2017 *)
LinearRecurrence[{0, 5}, {3, 5}, 30] (* Harvey P. Dale, Aug 01 2021 *)
PROG
(Magma) [ n le 2 select 2*n+1 else 5*Self(n-2): n in [1..29] ];
(PARI) x='x+O('x^30); Vec(x*(3+5*x)/(1-5*x^2)) \\ G. C. Greubel, Dec 21 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Klaus Brockhaus, Jul 21 2009
STATUS
approved