A047278 Numbers that are congruent to {1, 2, 6} mod 7.

1, 2, 6, 8, 9, 13, 15, 16, 20, 22, 23, 27, 29, 30, 34, 36, 37, 41, 43, 44, 48, 50, 51, 55, 57, 58, 62, 64, 65, 69, 71, 72, 76, 78, 79, 83, 85, 86, 90, 92, 93, 97, 99, 100, 104, 106, 107, 111, 113, 114, 118, 120, 121, 125, 127, 128, 132, 134, 135, 139, 141

Offset

1,2

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*(1+x+4*x^2+x^3) / ( (1+x+x^2)*(x-1)^2 ). - R. J. Mathar, Oct 25 2011

From Wesley Ivan Hurt, Jun 07 2016: (Start)

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.

a(n) = (21*n-15+6*cos(2*n*Pi/3)+4*sqrt(3)*sin(2*n*Pi/3))/9.

a(3k) = 7k-1, a(3k-1) = 7k-5, a(3k-2) = 7k-6. (End)

Maple

A047278:=n->(21*n-15+6*cos(2*n*Pi/3)+4*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047278(n), n=1..100); # Wesley Ivan Hurt, Jun 07 2016

Mathematica

Table[(21*n-15+6*Cos[2*n*Pi/3]+4*Sqrt[3]*Sin[2*n*Pi/3])/9, {n,
80}] (* Wesley Ivan Hurt, Jun 07 2016 *)
Select[Range[200], MemberQ[{1, 2, 6}, Mod[#, 7]]&] (* or *) LinearRecurrence[ {1, 0, 1, -1}, {1, 2, 6, 8}, 100] (* Harvey P. Dale, Dec 16 2018 *)

Prog

(Magma) [n : n in [1..150] | n mod 7 in [1, 2, 6]]; // Wesley Ivan Hurt, Jun 07 2016

Crossrefs

Sequence in context: A262981 A336745 A034591 * A242204 A172209 A107737

Adjacent sequences: A047275 A047276 A047277 * A047279 A047280 A047281

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved