A090223 Nonnegative integers with doubled multiples of 4.

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

Author

Wolfdieter Lang, Dec 01 2003

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A057353 and other floors of ratios references there.

Cf. A090222.

Programs

Magma

[4*n div 5: n in [0..80]]; // Bruno Berselli, Dec 07 2016

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 *)

PARI

a(n)=4*n\5 \\ Charles R Greathouse IV, Sep 02 2015

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