The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A087508 Number of k such that mod(k*n,3) = 1 for 0 <= k <= n. 6
 0, 1, 1, 0, 2, 2, 0, 3, 3, 0, 4, 4, 0, 5, 5, 0, 6, 6, 0, 7, 7, 0, 8, 8, 0, 9, 9, 0, 10, 10, 0, 11, 11, 0, 12, 12, 0, 13, 13, 0, 14, 14, 0, 15, 15, 0, 16, 16, 0, 17, 17, 0, 18, 18, 0, 19, 19, 0, 20, 20, 0, 21, 21, 0, 22, 22, 0, 23, 23, 0, 24, 24, 0, 25, 25, 0, 26, 26, 0, 27, 27, 0, 28, 28, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS G. C. Greubel, Table of n, a(n) for n = 0..10000 Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,-1). FORMULA a(n) = A000027(n) - A087509(n) - A087507(n). a(n) = (2/3)*(floor(n/3)+1)*(1-cos(2*Pi*n/3)). G.f.: x*(1 + x)/(1 - x^3)^2. - Arkadiusz Wesolowski, May 28 2013 a(n) = sin(n*Pi/3)*((4n+6)*sin(n*Pi/3)-sqrt(3)*cos(n*Pi))/9. - Wesley Ivan Hurt, Sep 24 2017 EXAMPLE a(4) = 2 because k=1 and k=4 satisfy the equation. MATHEMATICA LinearRecurrence[{0, 0, 2, 0, 0, -1}, {0, 1, 1, 0, 2, 2}, 100] (* Vincenzo Librandi, Sep 22 2015 *) Table[PadRight[{0}, 3, n], {n, 30}]//Flatten (* Harvey P. Dale, Jan 27 2021 *) PROG (PARI) concat(0, Vec((1+x)/(1-x^3)^2 +O(x^99))) \\ Charles R Greathouse IV, Oct 24 2014 (PARI) a(n) = sum(k=0, n, Mod(k*n, 3)==1); \\ Michel Marcus, Sep 27 2017 (Magma) I:=[0, 1, 1, 0, 2, 2]; [n le 6 select I[n] else 2*Self(n-3) - Self(n-6): n in [1..100]]; // Vincenzo Librandi, Sep 22 2015 (SageMath) @CachedFunction def A087508(n): if (n<6): return (0, 1, 1, 0, 2, 2)[n] else: return 2*A087508(n-3) - A087508(n-6) [A087508(n) for n in (0..100)] # G. C. Greubel, Sep 02 2022 CROSSREFS Cf. A000027, A087507, A087509. Sequence in context: A360048 A127899 A128615 * A095731 A048142 A071426 Adjacent sequences: A087505 A087506 A087507 * A087509 A087510 A087511 KEYWORD easy,nonn AUTHOR Paul Barry, Sep 11 2003 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 28 01:34 EDT 2024. Contains 372900 sequences. (Running on oeis4.)