A047275 Numbers that are congruent to {0, 1, 6} mod 7.

0, 1, 6, 7, 8, 13, 14, 15, 20, 21, 22, 27, 28, 29, 34, 35, 36, 41, 42, 43, 48, 49, 50, 55, 56, 57, 62, 63, 64, 69, 70, 71, 76, 77, 78, 83, 84, 85, 90, 91, 92, 97, 98, 99, 104, 105, 106, 111, 112, 113, 118, 119, 120, 125, 126, 127, 132, 133, 134, 139, 140

Offset

1,3

Comments

Nonnegative m such that floor(k*m^2/7) = k*floor(m^2/7), where k = 4, 5 or 6. See also the comment in A047299. [Bruno Berselli, Dec 03 2015]

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

Formula

G.f.: x^2*(1+5*x+x^2) / ((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-21+12*cos(2*n*Pi/3)+4*sqrt(3)*sin(2*n*Pi/3))/9.

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

Maple

A047275:=n->(21*n-21+12*cos(2*n*Pi/3)+4*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047275(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016

Mathematica

Select[Range[0, 120], Function[k, Mod[#, 7] == k] /@ Or[0, 1, 6] &] (* or *) Select[Range[0, 120], Function[k, Floor[k (#^2/7)] == k Floor[#^2/7]] /@ Or[4, 5, 6] &] (* Michael De Vlieger, Dec 03 2015 *)
LinearRecurrence[{1, 0, 1, -1}, {0, 1, 6, 7}, 100] (* Vincenzo Librandi, Jun 14 2016 *)

Prog

(PARI) concat(0, Vec(x^2*(1+5*x+x^2)/((1+x+x^2)*(x-1)^2) + O(x^100))) \\ Altug Alkan, Dec 03 2015
(Magma) [n : n in [0..150] | n mod 7 in [0, 1, 6]]; // Wesley Ivan Hurt, Jun 10 2016

Crossrefs

Cf. A047299.

Sequence in context: A083340 A118733 A328118 * A047590 A146329 A272344

Adjacent sequences: A047272 A047273 A047274 * A047276 A047277 A047278

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved