OFFSET
0,4
COMMENTS
Degrees of row-polynomials of array A090222.
a(n) is the number of full orbits completed by body A for n full orbits completed by body B in a celestial system with two orbiting bodies A and B with orbital resonance A:B equal to 4:5. This resonance is exhibited by the planets Kepler-90b and Kepler-90c in the planetary system of the star Kepler-90. - Felix Fröhlich, May 03 2021
LINKS
Felix Fröhlich, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).
FORMULA
a(n) = floor(4*n/5).
G.f.: x^2 *(1+x^2)*(1+x)/((1-x^5)*(1-x)) = (x^2)*(1-x^4)/((1-x^5)*(1-x)^2).
a(n) = n - 1 - A002266(n - 1). - Wesley Ivan Hurt, Nov 15 2013
a(n) = A057354(2*n). - R. J. Mathar, Jul 21 2020
5*a(n) = 4*n-2+A117444(n+2) . - R. J. Mathar, Jul 21 2020
Sum_{n>=2} (-1)^n/a(n) = (2*sqrt(2)-1)*Pi/8. - Amiram Eldar, Sep 30 2022
MAPLE
MATHEMATICA
Table[Floor[4n/5], {n, 0, 100}] (* Wesley Ivan Hurt, Nov 15 2013 *)
PROG
(PARI) a(n)=4*n\5 \\ Charles R Greathouse IV, Sep 02 2015
(Magma) [4*n div 5: n in [0..80]]; // Bruno Berselli, Dec 07 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Dec 01 2003
STATUS
approved