A047376 Numbers that are congruent to {1, 4, 5} mod 7.

1, 4, 5, 8, 11, 12, 15, 18, 19, 22, 25, 26, 29, 32, 33, 36, 39, 40, 43, 46, 47, 50, 53, 54, 57, 60, 61, 64, 67, 68, 71, 74, 75, 78, 81, 82, 85, 88, 89, 92, 95, 96, 99, 102, 103, 106, 109, 110, 113, 116, 117, 120, 123, 124, 127, 130, 131, 134, 137, 138, 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+3*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-12-6*cos(2*n*Pi/3)-2*sqrt(3)*sin(2*n*Pi/3))/9.

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

Maple

A047376:=n->(21*n-12-6*cos(2*n*Pi/3)-2*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047376(n), n=1..100); # Wesley Ivan Hurt, Jun 09 2016

Mathematica

Select[Range[200], MemberQ[{1, 4, 5}, Mod[#, 7]]&] (* Harvey P. Dale, Feb 24 2011 *)

Prog

(Magma) [n : n in [0..150] | n mod 7 in [1, 4, 5]]; // Wesley Ivan Hurt, Jun 09 2016

Crossrefs

Sequence in context: A050140 A190860 A191214 * A260989 A285566 A353044

Adjacent sequences: A047373 A047374 A047375 * A047377 A047378 A047379

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved