A057358 a(n) = floor(4*n/7).

0, 0, 1, 1, 2, 2, 3, 4, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 10, 10, 11, 12, 12, 13, 13, 14, 14, 15, 16, 16, 17, 17, 18, 18, 19, 20, 20, 21, 21, 22, 22, 23, 24, 24, 25, 25, 26, 26, 27, 28, 28, 29, 29, 30, 30, 31, 32, 32, 33, 33, 34, 34, 35, 36, 36, 37, 37, 38, 38, 39, 40, 40, 41, 41, 42

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

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 (1,0,0,0,0,0,1,-1)

Formula

G.f. x^2*(1+x^2+x^4+x^5) / ( (x^6+x^5+x^4+x^3+x^2+x+1)*(x-1)^2 ) - Numerator corrected by R. J. Mathar, Feb 20 2011

Sum_{n>=2} (-1)^n/a(n) = (Pi - 2*log(sqrt(2)+1))/(4*sqrt(2)). - Amiram Eldar, Sep 30 2022

Mathematica

Table[Floor[4*n/7], {n, 0, 50}] (* G. C. Greubel, Nov 02 2017 *)

Prog

(PARI) a(n)=4*n\7 \\ Charles R Greathouse IV, Sep 02 2015
(Magma) [Floor(4*n/7): 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: A321667 A194212 A194208 * A038128 A097337 A263574

Adjacent sequences: A057355 A057356 A057357 * A057359 A057360 A057361

Keyword

nonn,easy

Author

Mitch Harris

Status

approved