A057364 a(n) = floor(8*n/21).

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

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

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^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

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: A283302 A225593 A057360 * A060144 A107347 A320063

Adjacent sequences: A057361 A057362 A057363 * A057365 A057366 A057367

Keyword

nonn,easy

Author

Mitch Harris

Status

approved