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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
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
Sequence in context: A060143 A005206 A309077 * A014245 A350969 A096386
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)