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

0,4

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

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

Adjacent sequences: A090220 A090221 A090222 * A090224 A090225 A090226

Keyword

nonn,easy

Author

Wolfdieter Lang, Dec 01 2003

Status

approved