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A057362
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a(n) = floor(5*n/13).
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15
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0, 0, 0, 1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 13, 13, 13, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 18, 18, 18, 19, 19, 20, 20, 20, 21, 21, 21, 22, 22, 23, 23, 23, 24, 24, 25, 25, 25, 26, 26, 26, 27, 27, 28, 28, 28, 29
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OFFSET
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0,7
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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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Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,0,1,-1).
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FORMULA
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G.f.: x^3*(1 + x^3 + x^5 + x^8 + x^10) / ( (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 ). [Numerator corrected Feb 20 2011]
Sum_{n>=3} (-1)^(n+1)/a(n) = sqrt(1-2/sqrt(5))*Pi/5 + arccosh(7/2)/(2*sqrt(5)) + log(2)/5. - Amiram Eldar, Sep 30 2022
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MATHEMATICA
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Table[Floor[5*n/13], {n, 0, 50}] (* G. C. Greubel, Nov 02 2017 *)
LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1}, {0, 0, 0, 1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5}, 80] (* Harvey P. Dale, Dec 12 2021 *)
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PROG
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(Magma) [Floor(5*n/13): 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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