A047556 Numbers that are congruent to {3, 6, 7} mod 8.

3, 6, 7, 11, 14, 15, 19, 22, 23, 27, 30, 31, 35, 38, 39, 43, 46, 47, 51, 54, 55, 59, 62, 63, 67, 70, 71, 75, 78, 79, 83, 86, 87, 91, 94, 95, 99, 102, 103, 107, 110, 111, 115, 118, 119, 123, 126, 127, 131, 134, 135, 139, 142, 143, 147, 150, 151, 155, 158, 159

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

Maple

A047556:=n->(24*n-9*cos(2*n*Pi/3)-sqrt(3)*sin(2*n*Pi/3))/9: seq(A047556(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016

Mathematica

Select[Range[0, 150], MemberQ[{3, 6, 7}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 10 2016 *)
LinearRecurrence[{1,0,1,-1},{3,6,7,11},60] (* Harvey P. Dale, Sep 02 2024 *)

Formula

G.f.: x*(1+x)*(x^2+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) = (24*n-9*cos(2*n*Pi/3)-sqrt(3)*sin(2*n*Pi/3))/9.

a(3k) = 8k-1, a(3k-1) = 8k-2, a(3k-2) = 8k-5. (End)