A047458 Numbers that are congruent to {0, 3, 4} mod 8.

0, 3, 4, 8, 11, 12, 16, 19, 20, 24, 27, 28, 32, 35, 36, 40, 43, 44, 48, 51, 52, 56, 59, 60, 64, 67, 68, 72, 75, 76, 80, 83, 84, 88, 91, 92, 96, 99, 100, 104, 107, 108, 112, 115, 116, 120, 123, 124, 128, 131, 132, 136, 139, 140, 144, 147, 148, 152, 155, 156

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

G.f.: x^2*(3+x+4*x^2)/((1-x)^2*(1+x+x^2)). [Colin Barker, May 13 2012]

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

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

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

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

Maple

A047458:=n->8*n/3-3-cos(2*n*Pi/3)-sin(2*n*Pi/3)/(3*sqrt(3)): seq(A047458(n), n=1..100); # Wesley Ivan Hurt, Jun 09 2016

Mathematica

Select[Range[0, 150], MemberQ[{0, 3, 4}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 09 2016 *)
LinearRecurrence[{1, 0, 1, -1}, {0, 3, 4, 8}, 90] (* Harvey P. Dale, May 31 2017 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [0, 3, 4]]; // Wesley Ivan Hurt, Jun 09 2016

Crossrefs

Union of A008586 and A017101. - Michel Marcus, Jun 01 2017

Sequence in context: A222395 A222269 A310011 * A004014 A243177 A113294

Adjacent sequences: A047455 A047456 A047457 * A047459 A047460 A047461

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved