A047462 Numbers that are congruent to {0, 1, 4} mod 8.

0, 1, 4, 8, 9, 12, 16, 17, 20, 24, 25, 28, 32, 33, 36, 40, 41, 44, 48, 49, 52, 56, 57, 60, 64, 65, 68, 72, 73, 76, 80, 81, 84, 88, 89, 92, 96, 97, 100, 104, 105, 108, 112, 113, 116, 120, 121, 124, 128, 129, 132, 136, 137, 140, 144, 145, 148, 152, 153, 156

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, 1, 4]]; // Wesley Ivan Hurt, Jun 10 2016

Maple

A047462:=n->(24*n-33-3*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047462(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016

Mathematica

Select[Range[0, 150], MemberQ[{0, 1, 4}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 10 2016 *)

Formula

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

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-33-3*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9.

a(3k) = 8k-4, a(3k-1) = 8k-7, a(3k-2) = 8k-8. (End)