A047506 Numbers that are congruent to {4, 6, 7} mod 8.

4, 6, 7, 12, 14, 15, 20, 22, 23, 28, 30, 31, 36, 38, 39, 44, 46, 47, 52, 54, 55, 60, 62, 63, 68, 70, 71, 76, 78, 79, 84, 86, 87, 92, 94, 95, 100, 102, 103, 108, 110, 111, 116, 118, 119, 124, 126, 127, 132, 134, 135, 140, 142, 143, 148, 150, 151, 156, 158

Offset

1,1

Links

Table of n, a(n) for n=1..59.

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

Formula

G.f.: x*(4+2*x+x^2+x^3)/((1+x+x^2)*(x-1)^2). - R. J. Mathar, Nov 06 2015

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

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

a(n) = (24*n+3-12*cos(2*n*Pi/3)+2*sqrt(3)*sin(2*n*Pi/3))/9.

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

Maple

A047506:=n->(24*n+3-12*cos(2*n*Pi/3)+2*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047506(n), n=1..100); # Wesley Ivan Hurt, Jun 09 2016

Mathematica

Select[Range[0, 150], MemberQ[{4, 6, 7}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 09 2016 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [4, 6, 7]]; // Wesley Ivan Hurt, Jun 09 2016

Crossrefs

Sequence in context: A056853 A024566 A166457 * A310656 A102136 A102142

Adjacent sequences: A047503 A047504 A047505 * A047507 A047508 A047509

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved