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

1,2

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).

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

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 *)

Prog

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

Crossrefs

Cf. A008576, A047408.

Sequence in context: A137910 A022850 A008576 * A240603 A079392 A185723

Adjacent sequences: A047619 A047620 A047621 * A047623 A047624 A047625

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved