OFFSET
1,3
COMMENTS
n(n+1)(n+2)...(n+6) / (n + (n+1) + (n+2) + ... + (n+6)) is an integer.
LINKS
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
KEYWORD
nonn,easy
AUTHOR
Patrick De Geest, May 15 1998
STATUS
approved