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%I #18 Sep 08 2022 08:45:02
%S 0,0,1,1,2,3,3,4,4,5,6,6,7,8,8,9,9,10,11,11,12,12,13,14,14,15,16,16,
%T 17,17,18,19,19,20,20,21,22,22,23,24,24,25,25,26,27,27,28,28,29,30,30,
%U 31,32,32,33,33,34,35,35,36,36,37,38,38,39,40,40,41,41,42,43,43,44,44
%N a(n) = floor(8*n/13).
%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="/A057363/b057363.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_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 a(n) = a(n-1) + a(n-13) - a(n-14).
%F G.f.: x^2*(1+x)*(x^2 - x + 1)*(x^8 + x^7 + x^2 + 1)/( (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]
%t Table[Floor[8*n/13], {n, 0, 50}] (* _G. C. Greubel_, Nov 02 2017 *)
%t LinearRecurrence[{1,0,0,0,0,0,0,0,0,0,0,0,1,-1},{0,0,1,1,2,3,3,4,4,5,6,6,7,8},80] (* _Harvey P. Dale_, Jul 21 2020 *)
%o (PARI) a(n)=8*n\13 \\ _Charles R Greathouse IV_, Sep 02 2015
%o (Magma) [Floor(8*n/13): 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.
%Y Note that 20 appears twice. Different from A005206, A060143.
%K nonn,easy
%O 0,5
%A _Mitch Harris_
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