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A057355 a(n) = floor(3*n/5). 15
0, 0, 1, 1, 2, 3, 3, 4, 4, 5, 6, 6, 7, 7, 8, 9, 9, 10, 10, 11, 12, 12, 13, 13, 14, 15, 15, 16, 16, 17, 18, 18, 19, 19, 20, 21, 21, 22, 22, 23, 24, 24, 25, 25, 26, 27, 27, 28, 28, 29, 30, 30, 31, 31, 32, 33, 33, 34, 34, 35, 36, 36, 37, 37, 38, 39, 39, 40, 40, 41, 42, 42, 43, 43 (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, Addison-Wesley, NY, 1994.

LINKS

Table of n, a(n) for n=0..73.

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

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

FORMULA

G.f.: x^2*(1 + x^2 + x^3)/((1 - x)*(1 - x^5)) - Bruce Corrigan (scentman(AT)myfamily.com), Jul 03 2002

For all m>=0: a(5m)=0 mod 3; a(5m+1)=0 mod 3; a(5m+2)=1 mod 3; a(5m+3)=1 mod 3; a(5m+4)=2 mod 3.

a(n) = -1 + Sum_{k=0..n} (1/50)*(3*(k mod 5) - 7*((k+1) mod 5) + 13*((k+2) mod 5) - 7*((k+3) mod 5) + 13*((k+4) mod 5)) - Paolo P. Lava, Nov 17 2008

PROG

(PARI) a(n)=3*n\5 \\ Charles R Greathouse IV, Sep 02 2015

(MAGMA) [3*n div 5: n in [0..80]]; // Bruno Berselli, Dec 07 2016

CROSSREFS

Floors of other ratios: A004526, A002264, A002265, A004523, A057353, A057354, A057355, A057356, A057357, A057358, A057359, A057360, A057361, A057362, A057363, A057364, A057365, A057366, A057367.

Sequence in context: A219642 A139338 A244229 * A171975 A160511 A055930

Adjacent sequences:  A057352 A057353 A057354 * A057356 A057357 A057358

KEYWORD

nonn,easy

AUTHOR

Mitch Harris

STATUS

approved

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Last modified June 27 14:58 EDT 2017. Contains 288790 sequences.