A047347 Numbers that are congruent to {0, 1, 4} mod 7.

0, 1, 4, 7, 8, 11, 14, 15, 18, 21, 22, 25, 28, 29, 32, 35, 36, 39, 42, 43, 46, 49, 50, 53, 56, 57, 60, 63, 64, 67, 70, 71, 74, 77, 78, 81, 84, 85, 88, 91, 92, 95, 98, 99, 102, 105, 106, 109, 112, 113, 116, 119, 120, 123, 126, 127, 130, 133, 134, 137, 140, 141

Offset

1,3

Links

Table of n, a(n) for n=1..62.

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

Formula

G.f.: x^2*(1+3*x+3*x^2)/((1+x+x^2)*(x-1)^2). - R. J. Mathar, Oct 08 2011

From Wesley Ivan Hurt, Jun 10 2016: (Start)

a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.

a(n) = 7*n/3-3+4*sin(2*n*Pi/3)/(3*sqrt(3)).

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

Maple

A047347:=n->7*n/3-3+4*sin(2*n*Pi/3)/(3*sqrt(3)): seq(A047347(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016

Mathematica

Select[Range[0, 200], MemberQ[{0, 1, 4}, Mod[#, 7]]&] (* or *) LinearRecurrence[{1, 0, 1, -1}, {0, 1, 4, 7}, 100] (* Harvey P. Dale, Dec 05 2012 *)

Prog

(Magma) [n : n in [0..150] | n mod 7 in [0, 1, 4]]; // Wesley Ivan Hurt, Jun 10 2016

Crossrefs

Sequence in context: A128373 A080578 A288479 * A188376 A356088 A137362

Adjacent sequences: A047344 A047345 A047346 * A047348 A047349 A047350

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved