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%I #21 Sep 30 2022 07:47:45
%S 0,0,1,1,2,2,3,4,4,5,5,6,6,7,8,8,9,9,10,10,11,12,12,13,13,14,14,15,16,
%T 16,17,17,18,18,19,20,20,21,21,22,22,23,24,24,25,25,26,26,27,28,28,29,
%U 29,30,30,31,32,32,33,33,34,34,35,36,36,37,37,38,38,39,40,40,41,41,42
%N a(n) = floor(4*n/7).
%C The cyclic pattern (and numerator of the gf) is computed using Euclid's algorithm for GCD.
%D N. Dershowitz and E. M. Reingold, Calendrical Calculations, Cambridge University Press, 1997.
%D R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, Addison-Wesley, NY, 1994.
%H G. C. Greubel, <a href="/A057358/b057358.txt">Table of n, a(n) for n = 0..5000</a>
%H 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 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,1,-1)
%F G.f. x^2*(1+x^2+x^4+x^5) / ( (x^6+x^5+x^4+x^3+x^2+x+1)*(x-1)^2 ) - Numerator corrected by _R. J. Mathar_, Feb 20 2011
%F Sum_{n>=2} (-1)^n/a(n) = (Pi - 2*log(sqrt(2)+1))/(4*sqrt(2)). - _Amiram Eldar_, Sep 30 2022
%t Table[Floor[4*n/7], {n, 0, 50}] (* _G. C. Greubel_, Nov 02 2017 *)
%o (PARI) a(n)=4*n\7 \\ _Charles R Greathouse IV_, Sep 02 2015
%o (Magma) [Floor(4*n/7): n in [0..50]]; // _G. C. Greubel_, Nov 02 2017
%Y Floors of other ratios: A004526, A002264, A002265, A004523, A057353, A057354, A057355, A057356, A057357, A057358, A057359, A057360, A057361, A057362, A057363, A057364, A057365, A057366, A057367.
%K nonn,easy
%O 0,5
%A _Mitch Harris_
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