A047458 Numbers that are congruent to {0, 3, 4} mod 8.

0, 3, 4, 8, 11, 12, 16, 19, 20, 24, 27, 28, 32, 35, 36, 40, 43, 44, 48, 51, 52, 56, 59, 60, 64, 67, 68, 72, 75, 76, 80, 83, 84, 88, 91, 92, 96, 99, 100, 104, 107, 108, 112, 115, 116, 120, 123, 124, 128, 131, 132, 136, 139, 140, 144, 147, 148, 152, 155, 156

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Crossrefs

Union of A008586 and A017101. - Michel Marcus, Jun 01 2017

Programs

Magma

[n : n in [0..150] | n mod 8 in [0, 3, 4]]; // Wesley Ivan Hurt, Jun 09 2016

Maple

A047458:=n->8*n/3-3-cos(2*n*Pi/3)-sin(2*n*Pi/3)/(3*sqrt(3)): seq(A047458(n), n=1..100); # Wesley Ivan Hurt, Jun 09 2016

Mathematica

Select[Range[0, 150], MemberQ[{0, 3, 4}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 09 2016 *)
LinearRecurrence[{1,0,1,-1},{0,3,4,8},90] (* Harvey P. Dale, May 31 2017 *)

Formula

G.f.: x^2*(3+x+4*x^2)/((1-x)^2*(1+x+x^2)). [Colin Barker, May 13 2012]

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

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

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

a(3k) = 8k-4, a(3k-1) = 8k-5, a(3k-2) = 8k-8. (End)