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%I #16 Sep 08 2022 08:45:02
%S 0,0,1,1,2,3,3,4,4,5,6,6,7,8,8,9,9,10,11,11,12,13,13,14,14,15,16,16,
%T 17,17,18,19,19,20,21,21,22,22,23,24,24,25,26,26,27,27,28,29,29,30,30,
%U 31,32,32,33,34,34,35,35,36,37,37,38,39,39,40,40,41,42,42,43,43,44,45
%N a(n) = floor(13*n/21).
%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="/A057365/b057365.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_22">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,1,-1).
%F a(n) = a(n-1) + a(n-21) - a(n-22).
%F G.f.: x^2*(1 + x^2 + x^3 + x^5 + x^7 + x^8 + x^10 + x^11 + x^13 + x^15 + x^16 + x^18 + x^19)/( (1+x+x^2)*(x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)*(x^12 - x^11 + x^9 - x^8 + x^6 - x^4 + x^3 - x + 1)*(x-1)^2 ). [Numerator corrected Feb 20 2011]
%t Table[Floor[13*n/21], {n,0,50}] (* _G. C. Greubel_, Nov 02 2017 *)
%o (PARI) 13*n\21 \\ _Charles R Greathouse IV_, Sep 02 2015
%o (Magma) [Floor(12*n/21): 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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