A057362 a(n) = floor(5*n/13).
0, 0, 0, 1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 13, 13, 13, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 18, 18, 18, 19, 19, 20, 20, 20, 21, 21, 21, 22, 22, 23, 23, 23, 24, 24, 25, 25, 25, 26, 26, 26, 27, 27, 28, 28, 28, 29
Offset: 0
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 (1,0,0,0,0,0,0,0,0,0,0,0,1,-1).
Crossrefs
Programs
-
Magma
[Floor(5*n/13): n in [0..50]]; // G. C. Greubel, Nov 02 2017
-
Mathematica
Table[Floor[5*n/13], {n, 0, 50}] (* G. C. Greubel, Nov 02 2017 *) LinearRecurrence[{1,0,0,0,0,0,0,0,0,0,0,0,1,-1},{0,0,0,1,1,1,2,2,3,3,3,4,4,5},80] (* Harvey P. Dale, Dec 12 2021 *) -
PARI
a(n)=5*n\13 \\ Charles R Greathouse IV, Sep 02 2015
Formula
G.f.: x^3*(1 + x^3 + x^5 + x^8 + x^10) / ( (x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)*(x-1)^2 ). [Numerator corrected Feb 20 2011]
Sum_{n>=3} (-1)^(n+1)/a(n) = sqrt(1-2/sqrt(5))*Pi/5 + arccosh(7/2)/(2*sqrt(5)) + log(2)/5. - Amiram Eldar, Sep 30 2022
Comments