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

Author

Mitch Harris

Keywords

• nonn
• easy

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).

Crossrefs

Floors of other ratios: A004526, A002264, A002265, A004523, A057353, A057354, A057355, A057356, A057357, A057358, A057359, A057360, A057361, A057362, A057363, A057364, A057365, A057366, A057367.

Programs

Magma

[floor(8*n/21): n in [0..50]]; // G. C. Greubel, Nov 02 2017

Mathematica

Table[Floor[8 n/21],{n,0,80}] (* Harvey P. Dale, Jun 14 2011 *)

PARI

a(n)=8*n\21 \\ Charles R Greathouse IV, Jul 07 2011

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]