A057356 a(n) = floor(2*n/7).

0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 22, 22, 22

Offset

0,8

Comments

The cyclic pattern (and numerator of the gf) is computed using Euclid's algorithm for GCD.

References

R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, Addison-Wesley, NY, 1994.

N. Dershowitz and E. M. Reingold, Calendrical Calculations, Cambridge University Press, 1997.

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^4*(1+x)*(x^2-x+1)/( (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>=4} (-1)^n/a(n) = Pi/4 (A003881). - Amiram Eldar, Sep 30 2022

Mathematica

Table[Floor[2*n/7], {n, 0, 50}] (* G. C. Greubel, Nov 03 2017 *)

Prog

(PARI) a(n)=2*n\7 \\ Charles R Greathouse IV, Sep 24 2015
(Magma) [Floor(2*n/7): n in [0..50]]; // G. C. Greubel, Nov 03 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.

Cf. A003881.

Sequence in context: A269734 A066927 A060065 * A172274 A350843 A183138

Adjacent sequences: A057353 A057354 A057355 * A057357 A057358 A057359

Keyword

nonn,easy

Author

Mitch Harris

Status

approved