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

1,2

Comments

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

Links

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

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

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)

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 *)

Prog

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

Crossrefs

Cf. A004773.

Cf. A017077, A017101, A017137.

Sequence in context: A223732 A094740 A305849 * A054414 A136616 A121384

Adjacent sequences: A047397 A047398 A047399 * A047401 A047402 A047403

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved