A057361 a(n) = floor(5*n/8).

0, 0, 1, 1, 2, 3, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 10, 10, 11, 11, 12, 13, 13, 14, 15, 15, 16, 16, 17, 18, 18, 19, 20, 20, 21, 21, 22, 23, 23, 24, 25, 25, 26, 26, 27, 28, 28, 29, 30, 30, 31, 31, 32, 33, 33, 34, 35, 35, 36, 36, 37, 38, 38, 39, 40, 40, 41, 41, 42, 43, 43, 44, 45, 45

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

Formula

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

a(0)=0, a(1)=0, a(2)=1, a(3)=1, a(4)=2, a(5)=3, a(6)=3, a(7)=4, a(8)=5, a(n)=a(n-1)+a(n-8)-a(n-9). - Harvey P. Dale, Jul 18 2013

Sum_{n>=2} (-1)^n/a(n) = sqrt(2*(1+1/sqrt(5)))*Pi/10 - log(phi)/sqrt(5), where phi is the golden ratio (A001622). - Amiram Eldar, Sep 30 2022

Mathematica

Floor[(5*Range[0, 80])/8] (* or *) LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 1, -1}, {0, 0, 1, 1, 2, 3, 3, 4, 5}, 80] (* Harvey P. Dale, Jul 18 2013 *)

Prog

(PARI) a(n)=5*n\8 \\ Charles R Greathouse IV, Sep 02 2015
(Magma) [Floor(5*n/8): 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.

Cf. A001622.

Sequence in context: A123387 A123070 A367066 * A136409 A039729 A074065

Adjacent sequences: A057358 A057359 A057360 * A057362 A057363 A057364

Keyword

nonn,easy

Author

Mitch Harris

Status

approved