A047236 Numbers that are congruent to {1, 2, 4} mod 6.

1, 2, 4, 7, 8, 10, 13, 14, 16, 19, 20, 22, 25, 26, 28, 31, 32, 34, 37, 38, 40, 43, 44, 46, 49, 50, 52, 55, 56, 58, 61, 62, 64, 67, 68, 70, 73, 74, 76, 79, 80, 82, 85, 86, 88, 91, 92, 94, 97, 98, 100, 103, 104, 106, 109, 110, 112, 115, 116, 118, 121, 122, 124

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Programs

Magma

[n : n in [0..150] | n mod 6 in [1, 2, 4]]; // Wesley Ivan Hurt, Jun 10 2016

Maple

A047236:=n->(6*n-5-cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/3: seq(A047236(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016

Mathematica

Select[Range[0, 150], MemberQ[{1, 2, 4}, Mod[#, 6]] &] (* Wesley Ivan Hurt, Jun 10 2016 *)

Formula

G.f.: x*(1+x)*(2*x^2+1)/((1+x+x^2)*(x-1)^2). - R. J. Mathar, Oct 08 2011

From Wesley Ivan Hurt, Jun 10 2016: (Start)

a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.

a(n) = (6*n-5-cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/3.

a(3k) = 6k-2, a(3k-1) = 6k-4, a(3k-2) = 6k-5. (End)

Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/6 + log(2+sqrt(3))/(2*sqrt(3)) - log(2)/3. - Amiram Eldar, Dec 14 2021