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 A057365 a(n) = floor(13*n/21). 15
 0, 0, 1, 1, 2, 3, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 9, 10, 11, 11, 12, 13, 13, 14, 14, 15, 16, 16, 17, 17, 18, 19, 19, 20, 21, 21, 22, 22, 23, 24, 24, 25, 26, 26, 27, 27, 28, 29, 29, 30, 30, 31, 32, 32, 33, 34, 34, 35, 35, 36, 37, 37, 38, 39, 39, 40, 40, 41, 42, 42, 43, 43, 44, 45 (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 (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,1,-1). FORMULA a(n) = a(n-1) + a(n-21) - a(n-22). G.f.: x^2*(1 + x^2 + x^3 + x^5 + x^7 + x^8 + x^10 + x^11 + x^13 + x^15 + x^16 + x^18 + x^19)/( (1+x+x^2)*(x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)*(x^12 - x^11 + x^9 - x^8 + x^6 - x^4 + x^3 - x + 1)*(x-1)^2 ). [Numerator corrected Feb 20 2011] MATHEMATICA Table[Floor[13*n/21], {n, 0, 50}] (* G. C. Greubel, Nov 02 2017 *) PROG (PARI) 13*n\21 \\ Charles R Greathouse IV, Sep 02 2015 (Magma) [Floor(12*n/21): 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. Sequence in context: A060143 A005206 A309077 * A014245 A350969 A096386 Adjacent sequences: A057362 A057363 A057364 * A057366 A057367 A057368 KEYWORD nonn,easy AUTHOR Mitch Harris STATUS approved

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Last modified April 19 14:10 EDT 2024. Contains 371792 sequences. (Running on oeis4.)