A047413 Numbers that are congruent to {3, 4, 6} mod 8.

3, 4, 6, 11, 12, 14, 19, 20, 22, 27, 28, 30, 35, 36, 38, 43, 44, 46, 51, 52, 54, 59, 60, 62, 67, 68, 70, 75, 76, 78, 83, 84, 86, 91, 92, 94, 99, 100, 102, 107, 108, 110, 115, 116, 118, 123, 124, 126, 131, 132, 134, 139, 140, 142, 147, 148, 150, 155, 156, 158

Offset

1,1

Links

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

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

Formula

G.f.: x*(3+x+2*x^2+2*x^3)/((1+x+x^2)*(x-1)^2). - R. J. Mathar, Dec 05 2011

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

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

Maple

A047413:=n->(24*n-9-9*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047413(n), n=1..100); # Wesley Ivan Hurt, Jun 09 2016

Mathematica

Select[Range[0, 150], MemberQ[{3, 4, 6}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 09 2016 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [3, 4, 6]]; // Wesley Ivan Hurt, Jun 09 2016

Crossrefs

Sequence in context: A320688 A352734 A275418 * A331191 A294917 A115018

Adjacent sequences: A047410 A047411 A047412 * A047414 A047415 A047416

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved