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A057367 a(n) = floor(11*n/30). 16
0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18, 19, 19, 19, 20, 20, 20, 21, 21, 22, 22, 22, 23, 23, 23, 24, 24, 24, 25, 25, 26, 26, 26, 27, 27, 27, 28 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,7
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
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1).
FORMULA
a(n) = a(n-1) + a(n-30) - a(n-31).
G.f.: x^3*(1 + x^3 + x^6 + x^8 + x^11 + x^14 + x^17 + x^19 + x^22 + x^25 + x^27)/( (1+x)*(1+x+x^2)*(x^2-x+1)*(x^4+x^3+x^2+x+1)*(x^4-x^3+x^2-x+1)*(x^8 - x^7 + x^5 - x^4 + x^3 - x + 1)*(x^8+x^7-x^5-x^4-x^3+x+1)*(x-1)^2 ). [Corrected by R. J. Mathar, Feb 20 2011]
MAPLE
A057367:=n->floor(11*n/30); seq(A057367(k), k=0..100); # Wesley Ivan Hurt, Oct 29 2013
MATHEMATICA
Table[Floor[11n/30], {n, 0, 100}] (* Wesley Ivan Hurt, Oct 29 2013 *)
PROG
(PARI) a(n)=11*n\30 \\ Charles R Greathouse IV, Sep 02 2015
(Magma) [Floor(11*n/30): n in [0..50]]; // G. C. Greubel, Nov 03 2017
CROSSREFS
Similar pattern in Islamic leap years A057347. 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: A211339 A087739 A127763 * A032634 A057366 A189663
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)