A047386 Numbers that are congruent to {0, 2, 5} mod 7.

0, 2, 5, 7, 9, 12, 14, 16, 19, 21, 23, 26, 28, 30, 33, 35, 37, 40, 42, 44, 47, 49, 51, 54, 56, 58, 61, 63, 65, 68, 70, 72, 75, 77, 79, 82, 84, 86, 89, 91, 93, 96, 98, 100, 103, 105, 107, 110, 112, 114, 117, 119, 121, 124, 126, 128, 131, 133, 135, 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

a(n+1) = 3*n-2*floor(n/3)-(n^2 mod 3). - Gary Detlefs, Mar 19 2010

G.f.: x^2*(2+3*x+2*x^2)/((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>4.

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

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

Maple

seq(3*n-2*floor(n/3)-(n^2 mod 3), n=0..52); # Gary Detlefs, Mar 19 2010

Mathematica

Select[Range[0, 150], MemberQ[{0, 2, 5}, Mod[#, 7]] &] (* Wesley Ivan Hurt, Jun 09 2016 *)

Prog

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

Crossrefs

Cf. A011655. [Gary Detlefs, Mar 19 2010]

Sequence in context: A304498 A184743 A184749 * A187416 A243808 A275278

Adjacent sequences: A047383 A047384 A047385 * A047387 A047388 A047389

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved