A047386 Numbers that are congruent to {0, 2, 5} mod 7.

0, 2, 5, 7, 9, 12, 14, 16, 19, 21, 23, 26, 28, 30, 33, 35, 37, 40, 42, 44, 47, 49, 51, 54, 56, 58, 61, 63, 65, 68, 70, 72, 75, 77, 79, 82, 84, 86, 89, 91, 93, 96, 98, 100, 103, 105, 107, 110, 112, 114, 117, 119, 121, 124, 126, 128, 131, 133, 135, 138, 140

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A011655. [Gary Detlefs, Mar 19 2010]

Programs

Magma

[n : n in [0..150] | n mod 7 in [0, 2, 5]]; // Wesley Ivan Hurt, Jun 09 2016

Maple

seq(3*n-2*floor(n/3)-(n^2 mod 3), n=0..52); # Gary Detlefs, Mar 19 2010

Mathematica

Select[Range[0, 150], MemberQ[{0, 2, 5}, Mod[#, 7]] &] (* Wesley Ivan Hurt, Jun 09 2016 *)

Formula

a(n+1) = 3*n-2*floor(n/3)-(n^2 mod 3). - Gary Detlefs, Mar 19 2010

G.f.: x^2*(2+3*x+2*x^2)/((1+x+x^2)*(x-1)^2). - R. J. Mathar, Dec 05 2011

From Wesley Ivan Hurt, Jun 09 2016: (Start)

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

a(n) = (21*n-21+3*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9.

a(3k) = 7k-2, a(3k-1) = 7k-5, a(3k-2) = 7k-7. (End)