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A057364 a(n) = floor(8*n/21). 15
0, 0, 0, 1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 14, 14, 14, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18, 19, 19, 19, 20, 20, 20, 21, 21, 22, 22, 22, 23, 23, 24, 24, 24, 25, 25, 25, 26, 26, 27, 27, 27, 28, 28, 28, 29 (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, 0,0,0,0,0,1,-1).
FORMULA
a(n) = a(n-1) + a(n-21) - a(n-22).
G.f.: x^3*(1+x)*(x^4 - x^3 + x^2 - x + 1)*(x^13 + x^11 + x^3 + 1) / ( (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 by R. J. Mathar, Feb 20 2011]
MATHEMATICA
Table[Floor[8 n/21], {n, 0, 80}] (* Harvey P. Dale, Jun 14 2011 *)
PROG
(PARI) a(n)=8*n\21 \\ Charles R Greathouse IV, Jul 07 2011
(Magma) [floor(8*n/21): n in [0..50]]; // G. C. Greubel, Nov 02 2017
CROSSREFS
Sequence in context: A283302 A225593 A057360 * A060144 A107347 A320063
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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