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A057361 a(n) = floor(5*n/8). 15

%I #22 Sep 30 2022 07:47:53

%S 0,0,1,1,2,3,3,4,5,5,6,6,7,8,8,9,10,10,11,11,12,13,13,14,15,15,16,16,

%T 17,18,18,19,20,20,21,21,22,23,23,24,25,25,26,26,27,28,28,29,30,30,31,

%U 31,32,33,33,34,35,35,36,36,37,38,38,39,40,40,41,41,42,43,43,44,45,45

%N a(n) = floor(5*n/8).

%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="/A057361/b057361.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_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,1,-1).

%F G.f. x^2*(1+x^2+x^3+x^5+x^6) / ( (1+x)*(x^2+1)*(x^4+1)*(x-1)^2 ). - Numerator corrected Feb 20 2011

%F a(0)=0, a(1)=0, a(2)=1, a(3)=1, a(4)=2, a(5)=3, a(6)=3, a(7)=4, a(8)=5, a(n)=a(n-1)+a(n-8)-a(n-9). - _Harvey P. Dale_, Jul 18 2013

%F Sum_{n>=2} (-1)^n/a(n) = sqrt(2*(1+1/sqrt(5)))*Pi/10 - log(phi)/sqrt(5), where phi is the golden ratio (A001622). - _Amiram Eldar_, Sep 30 2022

%t Floor[(5*Range[0,80])/8] (* or *) LinearRecurrence[{1,0,0,0,0,0,0,1,-1},{0,0,1,1,2,3,3,4,5},80] (* _Harvey P. Dale_, Jul 18 2013 *)

%o (PARI) a(n)=5*n\8 \\ _Charles R Greathouse IV_, Sep 02 2015

%o (Magma) [Floor(5*n/8): 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 Cf. A001622.

%K nonn,easy

%O 0,5

%A _Mitch Harris_

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)