A047282 Numbers that are congruent to {1, 3, 6} mod 7.

1, 3, 6, 8, 10, 13, 15, 17, 20, 22, 24, 27, 29, 31, 34, 36, 38, 41, 43, 45, 48, 50, 52, 55, 57, 59, 62, 64, 66, 69, 71, 73, 76, 78, 80, 83, 85, 87, 90, 92, 94, 97, 99, 101, 104, 106, 108, 111, 113, 115, 118, 120, 122, 125, 127, 129, 132, 134, 136, 139, 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+2*x+3*x^2+x^3)/((1+x+x^2)*(x-1)^2). - R. J. Mathar, Oct 25 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) = (21*n-12+3*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9.

a(3*k) = 7*k-1, a(3*k-1) = 7*k-4, a(3*k-2) = 7*k-6. (End)

a(n) = 2*n - 1 + floor(n/3). - Wesley Ivan Hurt, Dec 28 2016

Maple

A047282:=n->(21*n-12+3*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9: seq(A047282(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016

Mathematica

Select[Range[0, 150], MemberQ[{1, 3, 6}, Mod[#, 7]] &] (* Wesley Ivan Hurt, Jun 10 2016 *)

Prog

(Magma) [n : n in [0..150] | n mod 7 in [1, 3, 6]]; // Wesley Ivan Hurt, Jun 10 2016

Crossrefs

Sequence in context: A189471 A169863 A304500 * A304497 A189937 A190325

Adjacent sequences: A047279 A047280 A047281 * A047283 A047284 A047285

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved