A087507 #{0<=k<=n: k*n is divisible by 3}.

1, 1, 1, 4, 2, 2, 7, 3, 3, 10, 4, 4, 13, 5, 5, 16, 6, 6, 19, 7, 7, 22, 8, 8, 25, 9, 9, 28, 10, 10, 31, 11, 11, 34, 12, 12, 37, 13, 13, 40, 14, 14, 43, 15, 15, 46, 16, 16, 49, 17, 17, 52, 18, 18, 55, 19, 19, 58, 20, 20, 61, 21, 21, 64, 22, 22, 67, 23, 23, 70, 24, 24, 73, 25, 25, 76

Offset: 0

Author

Paul Barry, Sep 11 2003

Keywords

• easy
• nonn

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,-1).

Crossrefs

Cf. A016777 (trisection).

Programs

PARI

Vec((2*x^3+x^2+x+1)/((x-1)^2*(x^2+x+1)^2) + O(x^100)) \\ Colin Barker, May 02 2015

Formula

a(n) = sum{k=0..n, if (mod(kn, 3)=0, 1, 0) }.

a(n) = floor(n/3)(5/3+4/3cos(2Pi*/3))+1.

a(n)+A087508(n)+A087509(n) = n.

a(n) = 2*a(n-3)-a(n-6) for n>5. - Colin Barker, May 02 2015

G.f.: (2*x^3+x^2+x+1) / ((x-1)^2*(x^2+x+1)^2). - Colin Barker, May 02 2015