A047480 Numbers that are congruent to {2, 5, 7} mod 8.

2, 5, 7, 10, 13, 15, 18, 21, 23, 26, 29, 31, 34, 37, 39, 42, 45, 47, 50, 53, 55, 58, 61, 63, 66, 69, 71, 74, 77, 79, 82, 85, 87, 90, 93, 95, 98, 101, 103, 106, 109, 111, 114, 117, 119, 122, 125, 127, 130, 133, 135, 138, 141, 143, 146, 149, 151, 154, 157, 159

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..3000
• Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Crossrefs

Different from A038127.

Cf. A047408.

Programs

Magma

[n : n in [0..150] | n mod 8 in [2, 5, 7]]; // Wesley Ivan Hurt, Jun 10 2016

Maple

A047480:=n->(24*n-6-3*cos(2*n*Pi/3)-sqrt(3)*sin(2*n*Pi/3))/9: seq(A047480(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016

Mathematica

Select[Range[0, 150], MemberQ[{2, 5, 7}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 10 2016 *)
Flatten[Table[8 n + {2, 5, 7}, {n, 0, 150}]] (* Vincenzo Librandi, Jun 12 2016 *)
LinearRecurrence[{1,0,1,-1},{2,5,7,10},100] (* Harvey P. Dale, Jun 18 2018 *)

Formula

G.f.: x*(1+x)*(x^2+x+2) / ((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-6-3*cos(2*n*Pi/3)-sqrt(3)*sin(2*n*Pi/3))/9.

a(3k) = 8k-1, a(3k-1) = 8k-3, a(3k-2) = 8k-6. (End)

a(n) = A047408(n) + 1. - Lorenzo Sauras Altuzarra, Jan 31 2023