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

1,2

Links

Table of n, a(n) for n=1..63.

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

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

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 *)

Prog

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

Crossrefs

Sequence in context: A116478 A207829 A207827 * A371638 A039581 A367498

Adjacent sequences: A047233 A047234 A047235 * A047237 A047238 A047239

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved