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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

G. C. Greubel, Table of n, a(n) for n = 0..5000

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

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).

Index entries for sequences related to Beatty sequences

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

Adjacent sequences:  A057364 A057365 A057366 * A057368 A057369 A057370

KEYWORD

nonn,easy

AUTHOR

Mitch Harris

STATUS

approved

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Last modified November 14 16:58 EST 2018. Contains 317210 sequences. (Running on oeis4.)