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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved
