A047474 Numbers that are congruent to {0, 2, 3} mod 8.

0, 2, 3, 8, 10, 11, 16, 18, 19, 24, 26, 27, 32, 34, 35, 40, 42, 43, 48, 50, 51, 56, 58, 59, 64, 66, 67, 72, 74, 75, 80, 82, 83, 88, 90, 91, 96, 98, 99, 104, 106, 107, 112, 114, 115, 120, 122, 123, 128, 130, 131, 136, 138, 139, 144, 146, 147, 152, 154, 155

Offset

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..1000

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

Formula

G.f.: x^2*(2+x+5*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) = (24*n-33-12*cos(2*n*Pi/3)+2*sqrt(3)*sin(2*n*Pi/3))/9.

a(3k) = 8k-5, a(3k-1) = 8k-6, a(3k-2) = 8k-8. (End)

Maple

A047474:=n->(24*n-33-12*cos(2*n*Pi/3)+2*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047474(n), n=1..100); # Wesley Ivan Hurt, Jun 09 2016

Mathematica

Select[Range[0, 150], MemberQ[{0, 2, 3}, Mod[#, 8]]&] (* Harvey P. Dale, Apr 08 2013 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [0, 2, 3]]; // Wesley Ivan Hurt, Jun 09 2016
(PARI) concat(0, Vec(x^2*(2+x+5*x^2)/((1-x)^2*(1+x+x^2)) + O(x^100))) \\ Colin Barker, Jun 12 2016

Crossrefs

Sequence in context: A028771 A023709 A317539 * A184797 A005454 A119187

Adjacent sequences: A047471 A047472 A047473 * A047475 A047476 A047477

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved