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A090223 Nonnegative integers with doubled multiples of 4.

%I A090223 #26 Sep 30 2022 07:48:01
%S A090223 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,
%T A090223 21,22,23,24,24,25,26,27,28,28,29,30,31,32,32,33,34,35,36,36,37,38,39,
%U A090223 40,40,41,42,43,44,44,45,46,47,48,48,49,50,51,52,52,53,54,55,56,56,57,58
%N A090223 Nonnegative integers with doubled multiples of 4.
%C A090223 Degrees of row-polynomials of array A090222.
%C A090223 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
%H A090223 Felix Fröhlich, <a href="/A090223/b090223.txt">Table of n, a(n) for n = 0..10000</a>
%H A090223 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,1,-1).
%F A090223 a(n) = floor(4*n/5).
%F A090223 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).
%F A090223 a(n) = n - 1 - A002266(n - 1). - _Wesley Ivan Hurt_, Nov 15 2013
%F A090223 a(n) = A057354(2*n). - _R. J. Mathar_, Jul 21 2020
%F A090223 5*a(n) = 4*n-2+A117444(n+2) . - _R. J. Mathar_, Jul 21 2020
%F A090223 Sum_{n>=2} (-1)^n/a(n) = (2*sqrt(2)-1)*Pi/8. - _Amiram Eldar_, Sep 30 2022
%p A090223 A090223:=n->floor(4*n/5); seq(A090223(n), n=0..100); # _Wesley Ivan Hurt_, Nov 15 2013
%t A090223 Table[Floor[4n/5], {n,0,100}] (* _Wesley Ivan Hurt_, Nov 15 2013 *)
%o A090223 (PARI) a(n)=4*n\5 \\ _Charles R Greathouse IV_, Sep 02 2015
%o A090223 (Magma) [4*n div 5: n in [0..80]]; // _Bruno Berselli_, Dec 07 2016
%Y A090223 Cf. A057353 and other floors of ratios references there.
%Y A090223 Cf. A090222.
%K A090223 nonn,easy
%O A090223 0,4
%A A090223 _Wolfdieter Lang_, Dec 01 2003