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A057361
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a(n) = floor(5*n/8).
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15
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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, 17, 18, 18, 19, 20, 20, 21, 21, 22, 23, 23, 24, 25, 25, 26, 26, 27, 28, 28, 29, 30, 30, 31, 31, 32, 33, 33, 34, 35, 35, 36, 36, 37, 38, 38, 39, 40, 40, 41, 41, 42, 43, 43, 44, 45, 45
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OFFSET
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0,5
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COMMENTS
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The cyclic pattern (and numerator of the gf) is computed using Euclid's algorithm for GCD.
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REFERENCES
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N. Dershowitz and E. M. Reingold, Calendrical Calculations, Cambridge University Press, 1997.
R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, Addison-Wesley, NY, 1994.
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LINKS
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FORMULA
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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
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
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
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MATHEMATICA
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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 *)
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PROG
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(Magma) [Floor(5*n/8): n in [0..50]]; // G. C. Greubel, Nov 02 2017
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CROSSREFS
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Floors of other ratios: A004526, A002264, A002265, A004523, A057353, A057354, A057355, A057356, A057357, A057358, A057359, A057360, A057361, A057362, A057363, A057364, A057365, A057366, A057367.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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