A047296 Numbers that are congruent to {3, 4, 6} mod 7.

3, 4, 6, 10, 11, 13, 17, 18, 20, 24, 25, 27, 31, 32, 34, 38, 39, 41, 45, 46, 48, 52, 53, 55, 59, 60, 62, 66, 67, 69, 73, 74, 76, 80, 81, 83, 87, 88, 90, 94, 95, 97, 101, 102, 104, 108, 109, 111, 115, 116, 118, 122, 123, 125, 129, 130, 132, 136, 137, 139, 143

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*(3+x+2*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-3) - a(n-4) for n>4.

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

a(3k) = 7k-1, a(3k-1) = 7k-3, a(3k-2) = 7k-4. (End)

Maple

A047296:=n->(21*n-3-6*cos(2*n*Pi/3)+4*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047296(n), n=1..100); # Wesley Ivan Hurt, Jun 07 2016

Mathematica

LinearRecurrence[{1, 0, 1, -1}, {3, 4, 6, 10}, 60] (* Harvey P. Dale, Apr 27 2015 *)

Prog

(Magma) [n : n in [1..150] | n mod 7 in [3, 4, 6]]; // Wesley Ivan Hurt, Jun 07 2016

Crossrefs

Sequence in context: A079325 A284528 A176865 * A368059 A301759 A322457

Adjacent sequences: A047293 A047294 A047295 * A047297 A047298 A047299

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved