A047408 Numbers that are congruent to {1, 4, 6} mod 8.

1, 4, 6, 9, 12, 14, 17, 20, 22, 25, 28, 30, 33, 36, 38, 41, 44, 46, 49, 52, 54, 57, 60, 62, 65, 68, 70, 73, 76, 78, 81, 84, 86, 89, 92, 94, 97, 100, 102, 105, 108, 110, 113, 116, 118, 121, 124, 126, 129, 132, 134, 137, 140, 142, 145, 148, 150, 153, 156, 158

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A047622.

Programs

Magma

[n : n in [0..150] | n mod 8 in [1, 4, 6]]; // Wesley Ivan Hurt, Jun 10 2016

Maple

A047408:=n->3*n-floor(n/3)-2; seq(A047408(k), k=1..100); # Wesley Ivan Hurt, Nov 07 2013

Mathematica

Table[3n-Floor[n/3]-2, {n, 100}] (* Wesley Ivan Hurt, Nov 07 2013 *)

Formula

G.f.: x*(1+3*x+2*x^2+2*x^3)/((1+x+x^2)*(x-1)^2). - R. J. Mathar, Dec 05 2011

a(n) = 3n - 2 - floor(n/3). - Wesley Ivan Hurt, Nov 07 2013

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

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

a(n) = (24*n-15-3*cos(2*n*Pi/3)-sqrt(3)*sin(2*n*Pi/3))/9.

a(3k) = 8k-2, a(3k-1) = 8k-4, a(3k-2) = 8k-7. (End)

E.g.f.: 2 + exp(x)*(8*x - 5)/3 - exp(-x/2)*(3*cos(sqrt(3)*x/2) + sqrt(3)*sin(sqrt(3)*x/2))/9. - Stefano Spezia, Mar 30 2023