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A057366 a(n) = floor(7*n/19).

%I A057366 #17 Sep 08 2022 08:45:02
%S A057366 0,0,0,1,1,1,2,2,2,3,3,4,4,4,5,5,5,6,6,7,7,7,8,8,8,9,9,9,10,10,11,11,
%T A057366 11,12,12,12,13,13,14,14,14,15,15,15,16,16,16,17,17,18,18,18,19,19,19,
%U A057366 20,20,21,21,21,22,22,22,23,23,23,24,24,25,25,25,26,26,26,27,27,28,28
%N A057366 a(n) = floor(7*n/19).
%C A057366 The cyclic pattern (and numerator of the gf) is computed using Euclid's algorithm for GCD.
%D A057366 N. Dershowitz and E. M. Reingold, Calendrical Calculations, Cambridge University Press, 1997.
%D A057366 R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, Addison-Wesley, NY, 1994.
%H A057366 G. C. Greubel, <a href="/A057366/b057366.txt">Table of n, a(n) for n = 0..5000</a>
%H A057366 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 A057366 <a href="/index/Rec#order_20">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, 0,0,1,-1).
%F A057366 a(n) = a(n-1) + a(n-19) - a(n-20).
%F A057366 G.f.: x^3*(x^2-x+1)*(x^14 + x^13 + x^12 - x^10 + x^8 + x^7 + x^6 + x + 1)/( (x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + 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 ). [Corrected by _R. J. Mathar_, Feb 20 2011]
%t A057366 Table[Floor[7*n/19], {n,0,50}] (* _G. C. Greubel_, Nov 03 2017 *)
%o A057366 (PARI) a(n)=7*n\19 \\ _Charles R Greathouse IV_, Sep 02 2015
%o A057366 (Magma) [Floor(7*n/19): n in [0..50]]; // _G. C. Greubel_, Nov 03 2017
%Y A057366 Similar pattern in Hebrew leap years A057349. Floors of other ratios: A004526, A002264, A002265, A004523, A057353, A057354, A057355, A057356, A057357, A057358, A057359, A057360, A057361, A057362, A057363, A057364, A057365, A057366, A057367.
%K A057366 nonn,easy
%O A057366 0,7
%A A057366 _Mitch Harris_