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A057361 a(n) = floor(5*n/8). 15
0, 0, 1, 1, 2, 3, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 10, 10, 11, 11, 12, 13, 13, 14, 15, 15, 16, 16, 17, 18, 18, 19, 20, 20, 21, 21, 22, 23, 23, 24, 25, 25, 26, 26, 27, 28, 28, 29, 30, 30, 31, 31, 32, 33, 33, 34, 35, 35, 36, 36, 37, 38, 38, 39, 40, 40, 41, 41, 42, 43, 43, 44, 45, 45 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
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
N. Dershowitz and E. M. Reingold, Calendrical Calculations Web Site.
FORMULA
G.f. x^2*(1+x^2+x^3+x^5+x^6) / ( (1+x)*(x^2+1)*(x^4+1)*(x-1)^2 ). - Numerator corrected Feb 20 2011
a(0)=0, a(1)=0, a(2)=1, a(3)=1, a(4)=2, a(5)=3, a(6)=3, a(7)=4, a(8)=5, a(n)=a(n-1)+a(n-8)-a(n-9). - Harvey P. Dale, Jul 18 2013
Sum_{n>=2} (-1)^n/a(n) = sqrt(2*(1+1/sqrt(5)))*Pi/10 - log(phi)/sqrt(5), where phi is the golden ratio (A001622). - Amiram Eldar, Sep 30 2022
MATHEMATICA
Floor[(5*Range[0, 80])/8] (* or *) LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 1, -1}, {0, 0, 1, 1, 2, 3, 3, 4, 5}, 80] (* Harvey P. Dale, Jul 18 2013 *)
PROG
(PARI) a(n)=5*n\8 \\ Charles R Greathouse IV, Sep 02 2015
(Magma) [Floor(5*n/8): n in [0..50]]; // G. C. Greubel, Nov 02 2017
CROSSREFS
Cf. A001622.
Sequence in context: A123387 A123070 A367066 * A136409 A039729 A074065
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified March 19 07:25 EDT 2024. Contains 370955 sequences. (Running on oeis4.)