A047278 Numbers that are congruent to {1, 2, 6} mod 7.

1, 2, 6, 8, 9, 13, 15, 16, 20, 22, 23, 27, 29, 30, 34, 36, 37, 41, 43, 44, 48, 50, 51, 55, 57, 58, 62, 64, 65, 69, 71, 72, 76, 78, 79, 83, 85, 86, 90, 92, 93, 97, 99, 100, 104, 106, 107, 111, 113, 114, 118, 120, 121, 125, 127, 128, 132, 134, 135, 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 [1..150] | n mod 7 in [1, 2, 6]]; // Wesley Ivan Hurt, Jun 07 2016

Maple

A047278:=n->(21*n-15+6*cos(2*n*Pi/3)+4*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047278(n), n=1..100); # Wesley Ivan Hurt, Jun 07 2016

Mathematica

Table[(21*n-15+6*Cos[2*n*Pi/3]+4*Sqrt[3]*Sin[2*n*Pi/3])/9, {n,
80}] (* Wesley Ivan Hurt, Jun 07 2016 *)
Select[Range[200],MemberQ[{1,2,6},Mod[#,7]]&] (* or *) LinearRecurrence[ {1,0,1,-1},{1,2,6,8},100] (* Harvey P. Dale, Dec 16 2018 *)

Formula

G.f.: x*(1+x+4*x^2+x^3) / ( (1+x+x^2)*(x-1)^2 ). - R. J. Mathar, Oct 25 2011

From Wesley Ivan Hurt, Jun 07 2016: (Start)

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.

a(n) = (21*n-15+6*cos(2*n*Pi/3)+4*sqrt(3)*sin(2*n*Pi/3))/9.

a(3k) = 7k-1, a(3k-1) = 7k-5, a(3k-2) = 7k-6. (End)