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Search: id:A057355
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| 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; listen)
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OFFSET
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0,5
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COMMENT
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The cyclic pattern (and numerator of the gf) is computed using Euclid's algorithm for GCD.
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REFERENCES
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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.
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LINKS
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N. Dershowitz and E. M. Reingold, Calendrical Calculations Web Site
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FORMULA
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G.f.: (1+x^2+x^3)*x^2/((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)} [From Paolo P. Lava (ppl(AT)spl.at), Nov 17 2008]
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CROSSREFS
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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: A156261 A071823 A139338 this_sequence A160511 A055930 A079952
Adjacent sequences: A057352 A057353 A057354 this_sequence A057356 A057357 A057358
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KEYWORD
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nonn,easy
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AUTHOR
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Mitch Harris (Harris.Mitchell(AT)mgh.harvard.edu)
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