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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Programs

Magma

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

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 *)

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)