A047375 Numbers that are congruent to {0, 4, 5} mod 7.

0, 4, 5, 7, 11, 12, 14, 18, 19, 21, 25, 26, 28, 32, 33, 35, 39, 40, 42, 46, 47, 49, 53, 54, 56, 60, 61, 63, 67, 68, 70, 74, 75, 77, 81, 82, 84, 88, 89, 91, 95, 96, 98, 102, 103, 105, 109, 110, 112, 116, 117, 119, 123, 124, 126, 130, 131, 133, 137, 138, 140

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^2*(4+x+2*x^2) / ((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-15-3*cos(2*n*Pi/3)-5*sqrt(3)*sin(2*n*Pi/3))/9.

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

Maple

A047375:=n->(21*n-15-3*cos(2*n*Pi/3)-5*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047375(n), n=1..100); # Wesley Ivan Hurt, Jun 09 2016

Mathematica

Select[Range[0, 150], MemberQ[{0, 4, 5}, Mod[#, 7]] &] (* Wesley Ivan Hurt, Jun 09 2016 *)

Prog

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

Crossrefs

Sequence in context: A032686 A074300 A344157 * A358805 A005487 A291741

Adjacent sequences: A047372 A047373 A047374 * A047376 A047377 A047378

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved