A047609 Numbers that are congruent to {0, 4, 5} mod 8.

0, 4, 5, 8, 12, 13, 16, 20, 21, 24, 28, 29, 32, 36, 37, 40, 44, 45, 48, 52, 53, 56, 60, 61, 64, 68, 69, 72, 76, 77, 80, 84, 85, 88, 92, 93, 96, 100, 101, 104, 108, 109, 112, 116, 117, 120, 124, 125, 128, 132, 133, 136, 140, 141, 144, 148, 149, 152, 156, 157

Offset

1,2

Links

Table of n, a(n) for n=1..60.

Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Formula

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

G.f.: x^2*(4+x+3*x^2)/((x-1)^2*(1+x+x^2)).

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

a(n) = (24*n-21-6*cos(2*n*Pi/3)-4*sqrt(3)*sin(2*n*Pi/3))/9.

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

Maple

A047609:=n->(24*n-21-6*cos(2*n*Pi/3)-4*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047609(n), n=1..100); # Wesley Ivan Hurt, Jun 09 2016

Mathematica

Select[Range[0, 150], MemberQ[{0, 4, 5}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 09 2016 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [0, 4, 5]]; // Wesley Ivan Hurt, Jun 09 2016

Crossrefs

Sequence in context: A130814 A183181 A310575 * A360993 A310576 A188095

Adjacent sequences: A047606 A047607 A047608 * A047610 A047611 A047612

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved