A047556 Numbers that are congruent to {3, 6, 7} mod 8.

3, 6, 7, 11, 14, 15, 19, 22, 23, 27, 30, 31, 35, 38, 39, 43, 46, 47, 51, 54, 55, 59, 62, 63, 67, 70, 71, 75, 78, 79, 83, 86, 87, 91, 94, 95, 99, 102, 103, 107, 110, 111, 115, 118, 119, 123, 126, 127, 131, 134, 135, 139, 142, 143, 147, 150, 151, 155, 158, 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

G.f.: x*(1+x)*(x^2+3) / ((1+x+x^2)*(x-1)^2). - R. J. Mathar, Oct 08 2011

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

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

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

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

Maple

A047556:=n->(24*n-9*cos(2*n*Pi/3)-sqrt(3)*sin(2*n*Pi/3))/9: seq(A047556(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016

Mathematica

Select[Range[0, 150], MemberQ[{3, 6, 7}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 10 2016 *)
LinearRecurrence[{1, 0, 1, -1}, {3, 6, 7, 11}, 60] (* Harvey P. Dale, Sep 02 2024 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [3, 6, 7]]; // Wesley Ivan Hurt, Jun 10 2016

Crossrefs

Sequence in context: A087642 A084349 A126003 * A255053 A292762 A374845

Adjacent sequences: A047553 A047554 A047555 * A047557 A047558 A047559

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved