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A057367 a(n) = floor(11*n/30).

%I A057367 #29 Sep 08 2022 08:45:02
%S A057367 0,0,0,1,1,1,2,2,2,3,3,4,4,4,5,5,5,6,6,6,7,7,8,8,8,9,9,9,10,10,11,11,
%T A057367 11,12,12,12,13,13,13,14,14,15,15,15,16,16,16,17,17,17,18,18,19,19,19,
%U A057367 20,20,20,21,21,22,22,22,23,23,23,24,24,24,25,25,26,26,26,27,27,27,28
%N A057367 a(n) = floor(11*n/30).
%C A057367 The cyclic pattern (and numerator of the gf) is computed using Euclid's algorithm for GCD.
%D A057367 N. Dershowitz and E. M. Reingold, Calendrical Calculations, Cambridge University Press, 1997.
%D A057367 R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, Addison-Wesley, NY, 1994.
%H A057367 G. C. Greubel, <a href="/A057367/b057367.txt">Table of n, a(n) for n = 0..5000</a>
%H A057367 <a href="/index/Rec#order_31">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1).
%H A057367 <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>
%F A057367 a(n) = a(n-1) + a(n-30) - a(n-31).
%F A057367 G.f.: x^3*(1 + x^3 + x^6 + x^8 + x^11 + x^14 + x^17 + x^19 + x^22 + x^25 + x^27)/( (1+x)*(1+x+x^2)*(x^2-x+1)*(x^4+x^3+x^2+x+1)*(x^4-x^3+x^2-x+1)*(x^8 - x^7 + x^5 - x^4 + x^3 - x + 1)*(x^8+x^7-x^5-x^4-x^3+x+1)*(x-1)^2 ). [Corrected by _R. J. Mathar_, Feb 20 2011]
%p A057367 A057367:=n->floor(11*n/30); seq(A057367(k), k=0..100); # _Wesley Ivan Hurt_, Oct 29 2013
%t A057367 Table[Floor[11n/30], {n,0,100}] (* _Wesley Ivan Hurt_, Oct 29 2013 *)
%o A057367 (PARI) a(n)=11*n\30 \\ _Charles R Greathouse IV_, Sep 02 2015
%o A057367 (Magma) [Floor(11*n/30): n in [0..50]]; // _G. C. Greubel_, Nov 03 2017
%Y A057367 Similar pattern in Islamic leap years A057347. Floors of other ratios: A004526, A002264, A002265, A004523, A057353, A057354, A057355, A057356, A057357, A057358, A057359, A057360, A057361, A057362, A057363, A057364, A057365, A057366, A057367.
%K A057367 nonn,easy
%O A057367 0,7
%A A057367 _Mitch Harris_