OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Ji Young Choi, A Generalization of Collatz Functions and Jacobsthal Numbers, J. Int. Seq., Vol. 21 (2018), Article 18.5.4.
Christopher R. Kitching, Henri Kauhanen, Jordan Abbott, Deepthi Gopal, Ricardo Bermúdez-Otero, and Tobias Galla, Estimating transmission noise on networks from stationary local order, arXiv:2405.12023 [cond-mat.stat-mech], 2024. See p. 48.
Index entries for linear recurrences with constant coefficients, signature (4,5).
FORMULA
G.f.: (1 - 4*x)/(1 - 4*x - 5*x^2).
a(n) = (5^n + 5*(-1)^n)/6.
a(n) = 5^(n-1) - a(n-1), a(0) = 1. - Jon E. Schoenfield, Feb 08 2015
MATHEMATICA
k=0; lst={k}; Do[k=5^n-k; AppendTo[lst, k], {n, 1, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 11 2008 *)
CoefficientList[Series[(1 - 4*x)/(1 - 4*x - 5*x^2), {x, 0, 50}], x] (* or *) Table[(5^n + 5*(-1)^n)/6, {n, 0, 30}] (* G. C. Greubel, Dec 30 2017 *)
PROG
(PARI) for(n=0, 30, print1((5^n + 5*(-1)^n)/6, ", ")) \\ G. C. Greubel, Dec 30 2017
(Magma) [(5^n + 5*(-1)^n)/6: n in [0..30]]; // G. C. Greubel, Dec 30 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mitch Harris, Jun 30 2005
EXTENSIONS
Corrected by Franklin T. Adams-Watters, Sep 18 2006
Edited by Jon E. Schoenfield, Feb 08 2015
STATUS
approved