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

1,1

Links

Table of n, a(n) for n=1..61.

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

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)

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 *)

Prog

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

Crossrefs

Cf. A153727 (first differences).

Sequence in context: A069001 A287181 A364732 * A101155 A065825 A113755

Adjacent sequences: A047375 A047376 A047377 * A047379 A047380 A047381

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved