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 A057363 a(n) = floor(8*n/13). 15
 0, 0, 1, 1, 2, 3, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 9, 10, 11, 11, 12, 12, 13, 14, 14, 15, 16, 16, 17, 17, 18, 19, 19, 20, 20, 21, 22, 22, 23, 24, 24, 25, 25, 26, 27, 27, 28, 28, 29, 30, 30, 31, 32, 32, 33, 33, 34, 35, 35, 36, 36, 37, 38, 38, 39, 40, 40, 41, 41, 42, 43, 43, 44, 44 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS The cyclic pattern (and numerator of the gf) is computed using Euclid's algorithm for GCD. REFERENCES 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. LINKS G. C. Greubel, Table of n, a(n) for n = 0..5000 N. Dershowitz and E. M. Reingold, Calendrical Calculations Web Site Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,0,1,-1). FORMULA a(n) = a(n-1) + a(n-13) - a(n-14). G.f.: x^2*(1+x)*(x^2 - x + 1)*(x^8 + x^7 + x^2 + 1)/( (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] MATHEMATICA Table[Floor[8*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, 1, 1, 2, 3, 3, 4, 4, 5, 6, 6, 7, 8}, 80] (* Harvey P. Dale, Jul 21 2020 *) PROG (PARI) a(n)=8*n\13 \\ Charles R Greathouse IV, Sep 02 2015 (Magma) [Floor(8*n/13): n in [0..50]]' // G. C. Greubel, Nov 02 2017 CROSSREFS Floors of other ratios: A004526, A002264, A002265, A004523, A057353, A057354, A057355, A057356, A057357, A057358, A057359, A057360, A057361, A057362, A057363, A057364, A057365, A057366, A057367. Note that 20 appears twice. Different from A005206, A060143. Sequence in context: A055930 A090638 A247908 * A073869 A060143 A005206 Adjacent sequences: A057360 A057361 A057362 * A057364 A057365 A057366 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified January 29 23:01 EST 2023. Contains 359939 sequences. (Running on oeis4.)