A032775 Numbers that are congruent to {0, 1, 2, 3, 5, 6} mod 7.

0, 1, 2, 3, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 47, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 73, 75, 76, 77, 78, 79, 80, 82, 83

Offset

1,3

Comments

n(n+1)(n+2)...(n+6) / (n + (n+1) + (n+2) + ... + (n+6)) is an integer.

Links

Table of n, a(n) for n=1..72.

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

Formula

Natural numbers minus '4, 11, 18, 25, ...' (= previous term + 7).

G.f.: x^2*(1+x+x^2+2*x^3+x^4+x^5) / ( (1+x)*(1+x+x^2)*(x^2-x+1)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011

From Wesley Ivan Hurt, Jun 15 2016: (Start)

a(n) = a(n-1) + a(n-6) - a(n-7) for n > 7.

a(n) = (42*n - 45 - 3*cos(n*Pi) + 12*cos(n*Pi/3) - 4*sqrt(3)*sin(2*n*Pi/3))/36.

a(6k) = 7k-1, a(6k-1) = 7k-2, a(6k-2) = 7k-4, a(6k-3) = 7k-5, a(6k-4) = 7k-6, a(6k-5) = 7k-7. (End)

Maple

A032775:=n->(42*n-45-3*cos(n*Pi)+12*cos(n*Pi/3)-4*sqrt(3)*sin(2*n*Pi/3))/36: seq(A032775(n), n=1..100); # Wesley Ivan Hurt, Jun 15 2016

Mathematica

Select[Range[0, 100], MemberQ[{0, 1, 2, 3, 5, 6}, Mod[#, 7]] &] (* Wesley Ivan Hurt, Jun 15 2016 *)
DeleteCases[Range[0, 100], _?(Mod[#, 7]==4&)] (* or *) LinearRecurrence[ {1, 0, 0, 0, 0, 1, -1}, {0, 1, 2, 3, 5, 6, 7}, 80] (* Harvey P. Dale, Sep 19 2020 *)

Prog

(Magma) [ n: n in [0..90] | n mod 7 in {0, 1, 2, 3, 5, 6} ]; // Vincenzo Librandi, Dec 29 2010

Crossrefs

Cf. A032774, A032776.

Sequence in context: A183295 A029927 A047334 * A057905 A353084 A039253

Adjacent sequences: A032772 A032773 A032774 * A032776 A032777 A032778

Keyword

nonn,easy

Author

Patrick De Geest, May 15 1998

Status

approved