A047400 Numbers that are congruent to {1, 3, 6} mod 8.

1, 3, 6, 9, 11, 14, 17, 19, 22, 25, 27, 30, 33, 35, 38, 41, 43, 46, 49, 51, 54, 57, 59, 62, 65, 67, 70, 73, 75, 78, 81, 83, 86, 89, 91, 94, 97, 99, 102, 105, 107, 110, 113, 115, 118, 121, 123, 126, 129, 131, 134, 137, 139, 142, 145, 147, 150, 153, 155, 158

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Union of A017077, A017101 and A017137. - R. J. Mathar, Apr 14 2008

Links

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

Crossrefs

Cf. A004773.

Cf. A017077, A017101, A017137.

Programs

Magma

[n: n in [1..300] | n mod 8 in [1, 3, 6]]; // Vincenzo Librandi, Mar 27 2011

Maple

A047400:=n->2*(12*n-9+sqrt(3)*sin(2*n*Pi/3))/9: seq(A047400(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016

Mathematica

Select[Range[0, 150], MemberQ[{1, 3, 6}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 10 2016 *)

PARI

a(n) = {x=8*floor((n-1)/3);if(n%3==1,x=x+1);if(n%3==2,x=x+3);if(n%3==0,x=x+6);x} \\ Michael B. Porter, Oct 02 2009

Formula

a(n) = A004773(n-1) + A004773(n). - Gary W. Adamson, Sep 13 2007

G.f.: x*(1+x)*(2x^2+x+1)/((-1+x)^2*(x^2+x+1)). a(n) = a(n-3)+8 for n>3. - R. J. Mathar, Apr 14 2008

From Wesley Ivan Hurt, Jun 10 2016: (Start)

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

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

a(3k) = 8k-2, a(3k-1) = 8k-5, a(3k-2) = 8k-7. (End)