A047249 Numbers that are congruent to {3, 4, 5} mod 6.

3, 4, 5, 9, 10, 11, 15, 16, 17, 21, 22, 23, 27, 28, 29, 33, 34, 35, 39, 40, 41, 45, 46, 47, 51, 52, 53, 57, 58, 59, 63, 64, 65, 69, 70, 71, 75, 76, 77, 81, 82, 83, 87, 88, 89, 93, 94, 95, 99, 100, 101, 105, 106, 107, 111, 112, 113, 117, 118, 119, 123, 124

Offset

1,1

Links

Table of n, a(n) for n=1..62.

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

Formula

G.f.: x*(3+x+x^2+x^3) / ((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) = 2*n-cos(2*n*Pi/3)+sin(2*n*Pi/3)/sqrt(3).

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

Sum_{n>=1} (-1)^(n+1)/a(n) = (9-2*sqrt(3))*Pi/36 + log(2)/6 - log(2+sqrt(3))/(2*sqrt(3)). - Amiram Eldar, Dec 16 2021

Maple

A047249:=n->2*n-cos(2*n*Pi/3)+sin(2*n*Pi/3)/sqrt(3): seq(A047249(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016

Mathematica

Select[Range[150], MemberQ[{3, 4, 5}, Mod[#, 6]]&] (* Harvey P. Dale, Nov 21 2012 *)

Prog

(Magma) [n : n in [0..150] | n mod 6 in [3..5]]; // Wesley Ivan Hurt, Jun 10 2016

Crossrefs

Sequence in context: A285161 A329781 A139531 * A327257 A228941 A236211

Adjacent sequences: A047246 A047247 A047248 * A047250 A047251 A047252

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved