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A057362 a(n) = floor(5*n/13).

%I A057362 #23 Sep 30 2022 07:47:57
%S A057362 0,0,0,1,1,1,2,2,3,3,3,4,4,5,5,5,6,6,6,7,7,8,8,8,9,9,10,10,10,11,11,
%T A057362 11,12,12,13,13,13,14,14,15,15,15,16,16,16,17,17,18,18,18,19,19,20,20,
%U A057362 20,21,21,21,22,22,23,23,23,24,24,25,25,25,26,26,26,27,27,28,28,28,29
%N A057362 a(n) = floor(5*n/13).
%C A057362 The cyclic pattern (and numerator of the gf) is computed using Euclid's algorithm for GCD.
%D A057362 N. Dershowitz and E. M. Reingold, Calendrical Calculations, Cambridge University Press, 1997.
%D A057362 R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, Addison-Wesley, NY, 1994.
%H A057362 G. C. Greubel, <a href="/A057362/b057362.txt">Table of n, a(n) for n = 0..5000</a>
%H A057362 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 A057362 <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,0,0,0,1,-1).
%F A057362 G.f.: x^3*(1 + x^3 + x^5 + x^8 + x^10) / ( (x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)*(x-1)^2 ). [Numerator corrected Feb 20 2011]
%F A057362 Sum_{n>=3} (-1)^(n+1)/a(n) = sqrt(1-2/sqrt(5))*Pi/5 + arccosh(7/2)/(2*sqrt(5)) + log(2)/5. - _Amiram Eldar_, Sep 30 2022
%t A057362 Table[Floor[5*n/13], {n, 0, 50}] (* _G. C. Greubel_, Nov 02 2017 *)
%t A057362 LinearRecurrence[{1,0,0,0,0,0,0,0,0,0,0,0,1,-1},{0,0,0,1,1,1,2,2,3,3,3,4,4,5},80] (* _Harvey P. Dale_, Dec 12 2021 *)
%o A057362 (PARI) a(n)=5*n\13 \\ _Charles R Greathouse IV_, Sep 02 2015
%o A057362 (Magma) [Floor(5*n/13): n in [0..50]]; // _G. C. Greubel_, Nov 02 2017
%Y A057362 Floors of other ratios: A004526, A002264, A002265, A004523, A057353, A057354, A057355, A057356, A057357, A057358, A057359, A057360, A057361, A057362, A057363, A057364, A057365, A057366, A057367.
%K A057362 nonn,easy
%O A057362 0,7
%A A057362 _Mitch Harris_