A047378 Numbers that are congruent to {2, 4, 5} mod 7.

2, 4, 5, 9, 11, 12, 16, 18, 19, 23, 25, 26, 30, 32, 33, 37, 39, 40, 44, 46, 47, 51, 53, 54, 58, 60, 61, 65, 67, 68, 72, 74, 75, 79, 81, 82, 86, 88, 89, 93, 95, 96, 100, 102, 103, 107, 109, 110, 114, 116, 117, 121, 123, 124, 128, 130, 131, 135, 137, 138, 142

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Crossrefs

Cf. A153727 (first differences).

Programs

Magma

[n : n in [0..150] | n mod 7 in [2, 4, 5]]; // Wesley Ivan Hurt, Jun 09 2016

Maple

A047378:=n->(21*n-9-9*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9: seq(A047378(n), n=1..100); # Wesley Ivan Hurt, Jun 09 2016

Mathematica

Select[Range[0, 150], MemberQ[{2, 4, 5}, Mod[#, 7]] &] (* Wesley Ivan Hurt, Jun 09 2016 *)
LinearRecurrence[{1,0,1,-1},{2,4,5,9},100] (* Harvey P. Dale, Jul 14 2022 *)

Formula

G.f.: x*(2+2*x+x^2+2*x^3)/((1+x+x^2)*(x-1)^2). - R. J. Mathar, Dec 04 2011

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

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

a(n) = (21*n-9-9*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9.

a(3k) = 7k-2, a(3k-1) = 7k-3, a(3k-2) = 7k-5. (End)