A047622 Numbers that are congruent to {0, 3, 5} mod 8.

0, 3, 5, 8, 11, 13, 16, 19, 21, 24, 27, 29, 32, 35, 37, 40, 43, 45, 48, 51, 53, 56, 59, 61, 64, 67, 69, 72, 75, 77, 80, 83, 85, 88, 91, 93, 96, 99, 101, 104, 107, 109, 112, 115, 117, 120, 123, 125, 128, 131, 133, 136, 139, 141, 144, 147, 149, 152, 155, 157

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Crossrefs

Cf. A008576, A047408.

Programs

Magma

[n : n in [0..150] | n mod 8 in [0, 3, 5]]; // Wesley Ivan Hurt, Jun 13 2016

Maple

seq(floor((8*n-7)/3), n=1..52); # Gary Detlefs, Mar 07 2010

Mathematica

Select[Range[0,150], MemberQ[{0,3,5}, Mod[#,8]]&] (* Harvey P. Dale, Oct 04 2012 *)
LinearRecurrence[{1, 0, 1, -1}, {0, 3, 5, 8}, 100] (* Vincenzo Librandi, Jun 14 2016 *)

Formula

From R. J. Mathar, Oct 18 2008: (Start)

G.f.: x^2*(3+2*x+3*x^2)/((1-x)^2*(1+x+x^2)).

a(n) = A008576(n-1), for n>1. (End)

a(n) = floor((8n-7)/3). - Gary Detlefs, Mar 07 2010

From Wesley Ivan Hurt, Jun 13 2016: (Start)

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

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

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

a(n) = A047408(n) - 1. - Lorenzo Sauras Altuzarra, Jan 31 2023

E.g.f.: 3 + (8/3)*exp(x)*(x - 1) - exp(-x/2)*(3*cos(sqrt(3)*x/2) + sqrt(3)*sin(sqrt(3)*x/2))/9. - Stefano Spezia, Mar 30 2023