OFFSET
1,2
COMMENTS
Integers n such that number of ways of drawing any number of nonintersecting chords joining n (labeled) points on a circle is divisible by n.
Corresponding values of A001006(n)/n are 1, 1, 6787979, ...
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..70
EXAMPLE
There are 142547559 ways to join 21 points on a circle by nonintersecting chords. Because of the fact that 142547559 is divisible by 21, 21 is a term of this sequence.
MATHEMATICA
lim = 100000; t = CoefficientList[Series[(1 - x - (1 - 2 x - 3 x^2)^(1/2))/(2 x^2), {x, 0, lim}], x]; Select[Range@ lim, Divisible[t[[# + 1]], #] &] (* Michael De Vlieger, Jan 09 2016, after Jean-François Alcover at A001006 *)
seq[kmax_] := Module[{mot1 = 1, mot2 = 2, mot, s = {1, 2}}, Do[mot3 = ((2*k+1)*mot2 + (3*k-3)*mot1)/(k+2); If[Divisible[mot3, k], AppendTo[s, k]]; mot1 = mot2; mot2 = mot3, {k, 3, kmax}]; s]; seq[10^5] (* Amiram Eldar, May 12 2024 *)
PROG
(PARI) lista(kmax) = {my(mot1 = 1, mot2 = 2, mot); print1(1, ", ", 2, ", "); for(k = 3, kmax, mot3 = ((2*k+1)*mot2 + (3*k-3)*mot1)/(k+2); if(!(mot3 % k), print1(k, ", ")); mot1 = mot2; mot2 = mot3); } \\ Amiram Eldar, May 12 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Altug Alkan, Jan 07 2016
EXTENSIONS
a(8)-a(17) from Michael De Vlieger, Jan 09 2016
a(18)-a(37) from Amiram Eldar, May 12 2024
STATUS
approved