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A090223
Nonnegative integers with doubled multiples of 4.
7
0, 0, 1, 2, 3, 4, 4, 5, 6, 7, 8, 8, 9, 10, 11, 12, 12, 13, 14, 15, 16, 16, 17, 18, 19, 20, 20, 21, 22, 23, 24, 24, 25, 26, 27, 28, 28, 29, 30, 31, 32, 32, 33, 34, 35, 36, 36, 37, 38, 39, 40, 40, 41, 42, 43, 44, 44, 45, 46, 47, 48, 48, 49, 50, 51, 52, 52, 53, 54, 55, 56, 56, 57, 58
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
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
A090223:=n->floor(4*n/5); seq(A090223(n), n=0..100); # Wesley Ivan Hurt, Nov 15 2013
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
Cf. A057353 and other floors of ratios references there.
Cf. A090222.
Sequence in context: A003004 A120507 A303787 * A366870 A171974 A232748
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Dec 01 2003
STATUS
approved