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A057353 a(n) = floor(3n/4). 26
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; text; internal format)
OFFSET

0,4

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

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

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)} - Paolo P. Lava, Nov 17 2008

a(n) = A002378(n) - A173562(n). - Reinhard Zumkeller, Feb 21 2010

a(n+1) = A140201(n) - A002265(n+1). - Reinhard Zumkeller, Jan 26 2011

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

a(n) = 1/8*(6*n + 2*cos((Pi*n)/2) + cos(Pi*n) - 2*sin((Pi*n)/2) - 3). - Ilya Gutkovskiy, Sep 18 2015

a(4n) = a(4n+1). - Altug Alkan, Sep 26 2015

MATHEMATICA

Table[Floor[3*n/4], {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Jan 28 2012 *)

PROG

(MAGMA) [Floor(3*n/4): n in [0..90]]; // Vincenzo Librandi, Feb 12 2012

(PARI) a(n)=3*n\4 \\ Charles R Greathouse IV, Sep 02 2015

CROSSREFS

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

Sequence in context: A215781 A215090 A083544 * A076539 A074184 A187329

Adjacent sequences:  A057350 A057351 A057352 * A057354 A057355 A057356

KEYWORD

nonn,easy

AUTHOR

Mitch Harris

STATUS

approved

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Last modified November 19 02:51 EST 2018. Contains 317332 sequences. (Running on oeis4.)