This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A057360 #30 Jan 10 2025 11:54:53
%S A057360 0,0,0,1,1,1,2,2,3,3,3,4,4,4,5,5,6,6,6,7,7,7,8,8,9,9,9,10,10,10,11,11,
%T A057360 12,12,12,13,13,13,14,14,15,15,15,16,16,16,17,17,18,18,18,19,19,19,20,
%U A057360 20,21,21,21,22,22,22,23,23,24,24,24,25,25,25,26,26,27,27,27,28,28,28
%N A057360 a(n) = floor(3*n/8).
%C A057360 The cyclic pattern (and numerator of the g.f.) is computed using Euclid's algorithm for GCD.
%D A057360 N. Dershowitz and E. M. Reingold, Calendrical Calculations, Cambridge University Press, 1997.
%D A057360 R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, Addison-Wesley, NY, 1994.
%H A057360 Vincenzo Librandi, <a href="/A057360/b057360.txt">Table of n, a(n) for n = 0..10000</a>
%H A057360 N. Dershowitz and E. M. Reingold, <a href="http://emr.cs.iit.edu/home/reingold/calendar-book/first-edition/">Calendrical Calculations Web Site</a>.
%H A057360 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,1,-1).
%F A057360 G.f.: x^3*(1+x^3+x^5) / ( (1+x)*(x^2+1)*(x^4+1)*(x-1)^2 ).
%F A057360 From _Wesley Ivan Hurt_, May 15 2015: (Start)
%F A057360 a(n) = a(n-1)+a(n-8)-a(n-9).
%F A057360 a(n) = A132292(A008585(n)), n>0.
%F A057360 a(n) = A002265(A032766(n)). (End)
%F A057360 Sum_{n>=3} (-1)^(n+1)/a(n) = Pi/(6*sqrt(3)) + log(3)/2. - _Amiram Eldar_, Sep 30 2022
%p A057360 A057360:=n->floor(3*n/8): seq(A057360(n), n=0..100); # _Wesley Ivan Hurt_, May 15 2015
%t A057360 Floor[3 Range[0, 100]/8] (* _Wesley Ivan Hurt_, May 15 2015 *)
%t A057360 LinearRecurrence[{1,0,0,0,0,0,0,1,-1},{0,0,0,1,1,1,2,2,3},80] (* _Harvey P. Dale_, Jan 10 2025 *)
%o A057360 (Magma) [Floor(3*n/8): n in [0..80]]; // _Vincenzo Librandi_, Jul 07 2011
%o A057360 (PARI) a(n)=3*n>>3 \\ _Charles R Greathouse IV_, Jul 07 2011
%Y A057360 Floors of other ratios: A004526, A002264, A002265, A004523, A057353, A057354, A057355, A057356, A057357, A057358, A057359, A057360, A057361, A057362, A057363, A057364, A057365, A057366, A057367.
%Y A057360 Cf. A008585, A032766, A132292.
%K A057360 nonn,easy
%O A057360 0,7
%A A057360 _Mitch Harris_
%E A057360 Numerator of g.f. corrected by _R. J. Mathar_, Feb 20 2011