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a(n) = floor(7*n/19).
15

%I #17 Sep 08 2022 08:45:02

%S 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 11,12,12,12,13,13,14,14,14,15,15,15,16,16,16,17,17,18,18,18,19,19,19,

%U 20,20,21,21,21,22,22,22,23,23,23,24,24,25,25,25,26,26,26,27,27,28,28

%N a(n) = floor(7*n/19).

%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="/A057366/b057366.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_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 a(n) = a(n-1) + a(n-19) - a(n-20).

%F 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 Table[Floor[7*n/19], {n,0,50}] (* _G. C. Greubel_, Nov 03 2017 *)

%o (PARI) a(n)=7*n\19 \\ _Charles R Greathouse IV_, Sep 02 2015

%o (Magma) [Floor(7*n/19): n in [0..50]]; // _G. C. Greubel_, Nov 03 2017

%Y 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 nonn,easy

%O 0,7

%A _Mitch Harris_