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

1,2

Links

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

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

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

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 *)

Prog

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

Crossrefs

Cf. A047622.

Sequence in context: A003622 A330215 A189533 * A060644 A122550 A191407

Adjacent sequences: A047405 A047406 A047407 * A047409 A047410 A047411

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved