A047598 Numbers that are congruent to {3, 4, 5} mod 8.

3, 4, 5, 11, 12, 13, 19, 20, 21, 27, 28, 29, 35, 36, 37, 43, 44, 45, 51, 52, 53, 59, 60, 61, 67, 68, 69, 75, 76, 77, 83, 84, 85, 91, 92, 93, 99, 100, 101, 107, 108, 109, 115, 116, 117, 123, 124, 125, 131, 132, 133, 139, 140, 141, 147, 148, 149, 155, 156, 157

Offset

1,1

Links

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

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

Formula

From Wesley Ivan Hurt, Jun 09 2016: (Start)

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

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

a(n) = (24*n-12-15*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9.

a(3k) = 8k-3, a(3k-1) = 8k-4, a(3k-2) = 8k-5. (End)

Maple

A047598:=n->(24*n-12-15*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047598(n), n=1..100); # Wesley Ivan Hurt, Jun 09 2016

Mathematica

Select[Range[0, 150], MemberQ[{3, 4, 5}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 09 2016 *)
LinearRecurrence[{1, 0, 1, -1}, {3, 4, 5, 11}, 80] (* Harvey P. Dale, May 20 2021 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [3..5]]; // Wesley Ivan Hurt, Jun 09 2016

Crossrefs

Sequence in context: A349005 A128920 A006288 * A283773 A214256 A067532

Adjacent sequences: A047595 A047596 A047597 * A047599 A047600 A047601

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved