A047619 Numbers that are congruent to {1, 2, 5} mod 8.

1, 2, 5, 9, 10, 13, 17, 18, 21, 25, 26, 29, 33, 34, 37, 41, 42, 45, 49, 50, 53, 57, 58, 61, 65, 66, 69, 73, 74, 77, 81, 82, 85, 89, 90, 93, 97, 98, 101, 105, 106, 109, 113, 114, 117, 121, 122, 125, 129, 130, 133, 137, 138, 141, 145, 146, 149, 153, 154, 157

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).

Programs

Magma

[n : n in [0..150] | n mod 8 in [1, 2, 5]]; // Wesley Ivan Hurt, Jun 09 2016

Maple

A047619:=n->(24*n-24-3*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047619(n), n=1..100); # Wesley Ivan Hurt, Jun 09 2016

Mathematica

Select[Range[0, 150], MemberQ[{1, 2, 5}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 09 2016 *)
Table[8 n + {1, 2, 5}, {n, 0, 100}]//Flatten (* Vincenzo Librandi, Jun 11 2016 *)
LinearRecurrence[{1,0,1,-1},{1,2,5,9},70] (* Harvey P. Dale, Aug 30 2021 *)

Formula

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

G.f.: x*(1+x+3*x^2+3*x^3)/((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-24-3*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9.

a(3k) = 8k-3, a(3k-1) = 8k-6, a(3k-2) = 8k-7. (End)