A047604 Numbers that are congruent to {2, 3, 5} mod 8.

2, 3, 5, 10, 11, 13, 18, 19, 21, 26, 27, 29, 34, 35, 37, 42, 43, 45, 50, 51, 53, 58, 59, 61, 66, 67, 69, 74, 75, 77, 82, 83, 85, 90, 91, 93, 98, 99, 101, 106, 107, 109, 114, 115, 117, 122, 123, 125, 130, 131, 133, 138, 139, 141, 146, 147, 149, 154, 155, 157

Offset

1,1

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

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

Formula

From Chai Wah Wu, May 29 2016: (Start)

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

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

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

a(n) = 8*n/3-2-cos(2*n*Pi/3)+5*sin(2*n*Pi/3)/(3*sqrt(3)).

a(3k) = 8k-3, a(3k-1) = 8k-5, a(3k-2) = 8k-6. (End)

Maple

A047604:=n->8*n/3-2-cos(2*n*Pi/3)+5*sin(2*n*Pi/3)/(3*sqrt(3)): seq(A047604(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016

Mathematica

Flatten[#+{2, 3, 5}&/@(8*Range[0, 20])] (* Harvey P. Dale, Oct 17 2013 *)
LinearRecurrence[{1, 0, 1, -1}, {2, 3, 5, 10}, 50] (* G. C. Greubel, May 29 2016 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [2, 3, 5]]; // Wesley Ivan Hurt, May 29 2016

Crossrefs

Sequence in context: A246392 A219860 A076681 * A104427 A259732 A192229

Adjacent sequences: A047601 A047602 A047603 * A047605 A047606 A047607

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved