A047523 Numbers that are congruent to {0, 1, 7} mod 8.

0, 1, 7, 8, 9, 15, 16, 17, 23, 24, 25, 31, 32, 33, 39, 40, 41, 47, 48, 49, 55, 56, 57, 63, 64, 65, 71, 72, 73, 79, 80, 81, 87, 88, 89, 95, 96, 97, 103, 104, 105, 111, 112, 113, 119, 120, 121, 127, 128, 129, 135, 136, 137, 143, 144, 145, 151, 152, 153, 159

Offset

1,3

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*(1+6*x+x^2) / ((1+x+x^2)*(x-1)^2). - R. J. Mathar, Oct 08 2011

From Wesley Ivan Hurt, Jun 13 2016: (Start)

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

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

a(3k) = 8k-1, a(3k-1) = 8k-7, a(3k-2) = 8k-8. (End)

Maple

A047523:=n->(24*n-24+15*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*Pi*n/3))/9: seq(A047523(n), n=1..100); # Wesley Ivan Hurt, Jun 13 2016

Mathematica

Select[Range[0, 150], MemberQ[{0, 1, 7}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 13 2016 *)
LinearRecurrence[{1, 0, 1, -1}, {0, 1, 7, 8}, 100] (* Vincenzo Librandi, Jun 14 2016 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [0, 1, 7]]; // Wesley Ivan Hurt, Jun 13 2016

Crossrefs

Sequence in context: A037369 A076599 A067197 * A108177 A165480 A285468

Adjacent sequences: A047520 A047521 A047522 * A047524 A047525 A047526

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved