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0, 0, 1, 2, 3, 3, 4, 5, 6, 6, 7, 8, 9, 9, 10, 11, 12, 12, 13, 14, 15, 15, 16, 17, 18, 18, 19, 20, 21, 21, 22, 23, 24, 24, 25, 26, 27, 27, 28, 29, 30, 30, 31, 32, 33, 33, 34, 35, 36, 36, 37, 38, 39, 39, 40, 41, 42, 42, 43, 44, 45, 45, 46, 47, 48, 48, 49, 50, 51, 51, 52, 53, 54
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| The cyclic pattern (and numerator of the gf) is computed using Euclid's algorithm for GCD.
a(n) = A002378(n) - A173562(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 21 2010]
a(n+1) = A140201(n) - A002265(n+1). - Reinhard Zumkeller, Jan 26 2011
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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.
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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 sequences related to Beatty sequences
Index to sequences with linear recurrences with constant coefficients, signature (1,0,0,1,-1).
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FORMULA
| G.f.: (1+x+x^2)*x^2/((1-x)*(1-x^4)) - Bruce Corrigan (scentman(AT)myfamily.com), Jul 03 2002
For all m>=0 a(4m)=0 mod 3; a(4m+1)=0 mod 3; a(4m+2)= 1 mod 3; a(4m+3) = 2 mod 3
a(n)=-1+Sum{k=0..n}{(1/8)*((k mod 4)+((k+1) mod 4)-((k+2) mod 4)+3*((k+3) mod 4)} [From Paolo P. Lava (paoloplava(AT)gmail.com), Nov 17 2008]
a(n) = n-1 - A002265(n-1) = ( A007310(n) + A057077(n+1) )/4 for n>0. a(n) = a(n-1)+a(n-4)-a(n-5) for n>4. - Bruno Berselli, Jan 28 2011
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MATHEMATICA
| Table[Floor[3*n/4], {n, 0, 100}] (* From Vladimir Joseph Stephan Orlovsky, Jan 28 2012 *)
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PROG
| (MAGMA) [Floor(3*n/4): n in [0..90]]; // Vincenzo Librandi, Feb 12 2012
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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: A086525 A120503 A083544 * A076539 A074184 A187329
Adjacent sequences: A057350 A057351 A057352 * A057354 A057355 A057356
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KEYWORD
| nonn,easy,changed
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AUTHOR
| Mitch Harris (Harris.Mitchell(AT)mgh.harvard.edu)
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