A047282 Numbers that are congruent to {1, 3, 6} mod 7.

1, 3, 6, 8, 10, 13, 15, 17, 20, 22, 24, 27, 29, 31, 34, 36, 38, 41, 43, 45, 48, 50, 52, 55, 57, 59, 62, 64, 66, 69, 71, 73, 76, 78, 80, 83, 85, 87, 90, 92, 94, 97, 99, 101, 104, 106, 108, 111, 113, 115, 118, 120, 122, 125, 127, 129, 132, 134, 136, 139, 141

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 7 in [1, 3, 6]]; // Wesley Ivan Hurt, Jun 10 2016

Maple

A047282:=n->(21*n-12+3*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9: seq(A047282(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016

Mathematica

Select[Range[0, 150], MemberQ[{1, 3, 6}, Mod[#, 7]] &] (* Wesley Ivan Hurt, Jun 10 2016 *)

Formula

G.f.: x*(1+2*x+3*x^2+x^3)/((1+x+x^2)*(x-1)^2). - R. J. Mathar, Oct 25 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) = (21*n-12+3*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9.

a(3*k) = 7*k-1, a(3*k-1) = 7*k-4, a(3*k-2) = 7*k-6. (End)

a(n) = 2*n - 1 + floor(n/3). - Wesley Ivan Hurt, Dec 28 2016