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

Author

Mitch Harris

Keywords

• nonn
• easy

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).

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.

Programs

Magma

[Floor(3*n/8): n in [0..80]]; // Vincenzo Librandi, Jul 07 2011

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 *)
LinearRecurrence[{1,0,0,0,0,0,0,1,-1},{0,0,0,1,1,1,2,2,3},80] (* Harvey P. Dale, Jan 10 2025 *)

PARI

a(n)=3*n>>3 \\ Charles R Greathouse IV, Jul 07 2011

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

Extensions

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