A047528 Numbers that are congruent to {0, 3, 7} mod 8.

0, 3, 7, 8, 11, 15, 16, 19, 23, 24, 27, 31, 32, 35, 39, 40, 43, 47, 48, 51, 55, 56, 59, 63, 64, 67, 71, 72, 75, 79, 80, 83, 87, 88, 91, 95, 96, 99, 103, 104, 107, 111, 112, 115, 119, 120, 123, 127, 128, 131, 135, 136, 139, 143, 144, 147, 151, 152, 155, 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 [0, 3, 7]]; // Wesley Ivan Hurt, Jun 10 2016

Maple

A047528:=n->8*n/3-2+cos(2*n*Pi/3)-sin(2*n*Pi/3)/(3*sqrt(3)): seq(A047528(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016

Mathematica

Select[Range[0, 150], MemberQ[{0, 3, 7}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 10 2016 *)
LinearRecurrence[{1,0,1,-1},{0,3,7,8},70] (* Harvey P. Dale, Jun 12 2019 *)

Formula

G.f.: x^2*(x+3)*(1+x) / ((1+x+x^2)*(x-1)^2). - R. J. Mathar, Jul 10 2015

From Wesley Ivan Hurt, Jun 10 2016: (Start)

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

a(n) = 8*n/3-2+cos(2*n*Pi/3)-sin(2*n*Pi/3)/(3*sqrt(3)).

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