A047387 Numbers that are congruent to {1, 2, 5} mod 7.

1, 2, 5, 8, 9, 12, 15, 16, 19, 22, 23, 26, 29, 30, 33, 36, 37, 40, 43, 44, 47, 50, 51, 54, 57, 58, 61, 64, 65, 68, 71, 72, 75, 78, 79, 82, 85, 86, 89, 92, 93, 96, 99, 100, 103, 106, 107, 110, 113, 114, 117, 120, 121, 124, 127, 128, 131, 134, 135, 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+x+3*x^2+2*x^3)/((1+x+x^2)*(x-1)^2). - R. J. Mathar, Dec 05 2011

From Wesley Ivan Hurt, Jun 09 2016: (Start)

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

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

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

Maple

A047387:=n->7*n/3-2+4*sin(2*n*Pi/3)/(3*sqrt(3)): seq(A047387(n), n=1..100); # Wesley Ivan Hurt, Jun 09 2016

Mathematica

Select[Range[200], MemberQ[{1, 2, 5}, Mod[#, 7]]&] (* or *) LinearRecurrence[ {1, 0, 1, -1}, {1, 2, 5, 8}, 90] (* Harvey P. Dale, Jun 05 2014 *)

Prog

(Magma) [n : n in [0..150] | n mod 7 in [1, 2, 5]]; // Wesley Ivan Hurt, Jun 09 2016

Crossrefs

Sequence in context: A183234 A108968 A289628 * A063282 A276882 A045928

Adjacent sequences: A047384 A047385 A047386 * A047388 A047389 A047390

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved