A057360 a(n) = floor(3*n/8).

0, 0, 0, 1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 18, 18, 18, 19, 19, 19, 20, 20, 21, 21, 21, 22, 22, 22, 23, 23, 24, 24, 24, 25, 25, 25, 26, 26, 27, 27, 27, 28, 28, 28

Offset

0,7

Comments

The cyclic pattern (and numerator of the g.f.) 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

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

N. Dershowitz and E. M. Reingold, Calendrical Calculations Web Site.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,1,-1).

Formula

G.f.: x^3*(1+x^3+x^5) / ( (1+x)*(x^2+1)*(x^4+1)*(x-1)^2 ).

From Wesley Ivan Hurt, May 15 2015: (Start)

a(n) = a(n-1)+a(n-8)-a(n-9).

a(n) = A132292(A008585(n)), n>0.

a(n) = A002265(A032766(n)). (End)

Sum_{n>=3} (-1)^(n+1)/a(n) = Pi/(6*sqrt(3)) + log(3)/2. - Amiram Eldar, Sep 30 2022

Maple

A057360:=n->floor(3*n/8): seq(A057360(n), n=0..100); # Wesley Ivan Hurt, May 15 2015

Mathematica

Floor[3 Range[0, 100]/8] (* Wesley Ivan Hurt, May 15 2015 *)

Prog

(Magma) [Floor(3*n/8): n in [0..80]]; // Vincenzo Librandi, Jul 07 2011
(PARI) a(n)=3*n>>3 \\ Charles R Greathouse IV, Jul 07 2011

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. A008585, A032766, A132292.

Sequence in context: A053620 A283302 A225593 * A057364 A060144 A107347

Adjacent sequences: A057357 A057358 A057359 * A057361 A057362 A057363

Keyword

nonn,easy

Author

Mitch Harris

Extensions

Numerator of g.f. corrected by R. J. Mathar, Feb 20 2011

Status

approved