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A057366 a(n) = floor(7*n/19). 15
0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 14, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 18, 18, 18, 19, 19, 19, 20, 20, 21, 21, 21, 22, 22, 22, 23, 23, 23, 24, 24, 25, 25, 25, 26, 26, 26, 27, 27, 28, 28 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,7
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, 0,0,1,-1).
FORMULA
a(n) = a(n-1) + a(n-19) - a(n-20).
G.f.: x^3*(x^2-x+1)*(x^14 + x^13 + x^12 - x^10 + x^8 + x^7 + x^6 + x + 1)/( (x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + 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 ). [Corrected by R. J. Mathar, Feb 20 2011]
MATHEMATICA
Table[Floor[7*n/19], {n, 0, 50}] (* G. C. Greubel, Nov 03 2017 *)
PROG
(PARI) a(n)=7*n\19 \\ Charles R Greathouse IV, Sep 02 2015
(Magma) [Floor(7*n/19): n in [0..50]]; // G. C. Greubel, Nov 03 2017
CROSSREFS
Similar pattern in Hebrew leap years A057349. 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: A127763 A057367 A032634 * A189663 A341440 A355028
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified March 19 03:33 EDT 2024. Contains 370952 sequences. (Running on oeis4.)