A047543 Numbers that are congruent to {3, 4, 7} mod 8.

3, 4, 7, 11, 12, 15, 19, 20, 23, 27, 28, 31, 35, 36, 39, 43, 44, 47, 51, 52, 55, 59, 60, 63, 67, 68, 71, 75, 76, 79, 83, 84, 87, 91, 92, 95, 99, 100, 103, 107, 108, 111, 115, 116, 119, 123, 124, 127, 131, 132, 135, 139, 140, 143, 147, 148, 151, 155, 156, 159

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+3*x^2+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-6-3*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9.

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

Maple

A047543:=n->(24*n-6-3*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047543(n), n=1..100); # Wesley Ivan Hurt, Jun 09 2016

Mathematica

Select[Range[0, 150], MemberQ[{3, 4, 7}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 09 2016 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [3, 4, 7]]; // Wesley Ivan Hurt, Jun 09 2016

Crossrefs

Sequence in context: A328379 A080591 A291063 * A030489 A132841 A274280

Adjacent sequences: A047540 A047541 A047542 * A047544 A047545 A047546

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved