A047590 Numbers that are congruent to {0, 6, 7} mod 8.

0, 6, 7, 8, 14, 15, 16, 22, 23, 24, 30, 31, 32, 38, 39, 40, 46, 47, 48, 54, 55, 56, 62, 63, 64, 70, 71, 72, 78, 79, 80, 86, 87, 88, 94, 95, 96, 102, 103, 104, 110, 111, 112, 118, 119, 120, 126, 127, 128, 134, 135, 136, 142, 143, 144, 150, 151, 152, 158, 159

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

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

G.f.: x^2*(6+x+x^2)/((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-9-10*sqrt(3)*sin(2*n*Pi/3))/9.

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

Maple

A047590:=n->(24*n-9-10*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047590(n), n=1..100); # Wesley Ivan Hurt, Jun 09 2016

Mathematica

Select[Range[0, 150], MemberQ[{0, 6, 7}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 09 2016 *)
LinearRecurrence[{1, 0, 1, -1}, {0, 6, 7, 8}, 100] (* Harvey P. Dale, Nov 18 2020 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [0, 6, 7]]; // Wesley Ivan Hurt, Jun 09 2016

Crossrefs

Sequence in context: A118733 A328118 A047275 * A146329 A272344 A133893

Adjacent sequences: A047587 A047588 A047589 * A047591 A047592 A047593

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved