

A057363


a(n) = floor(8*n/13).


15



0, 0, 1, 1, 2, 3, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 9, 10, 11, 11, 12, 12, 13, 14, 14, 15, 16, 16, 17, 17, 18, 19, 19, 20, 20, 21, 22, 22, 23, 24, 24, 25, 25, 26, 27, 27, 28, 28, 29, 30, 30, 31, 32, 32, 33, 33, 34, 35, 35, 36, 36, 37, 38, 38, 39, 40, 40, 41, 41, 42, 43, 43, 44, 44
(list;
graph;
refs;
listen;
history;
text;
internal format)



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, AddisonWesley, NY, 1994.


LINKS

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


FORMULA

a(n) = a(n1) + a(n13)  a(n14).
G.f.: x^2*(1+x)*(x^2  x + 1)*(x^8 + x^7 + x^2 + 1)/( (x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)*(x1)^2 ). [Numerator corrected Feb 20 2011]


MATHEMATICA

Table[Floor[8*n/13], {n, 0, 50}] (* G. C. Greubel, Nov 02 2017 *)
LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1}, {0, 0, 1, 1, 2, 3, 3, 4, 4, 5, 6, 6, 7, 8}, 80] (* Harvey P. Dale, Jul 21 2020 *)


PROG

(Magma) [Floor(8*n/13): 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.


KEYWORD

nonn,easy


AUTHOR



STATUS

approved



