A199932 - OEIS

%I #17 Mar 30 2023 00:49:37

%S 1,3,5,12,17,47,65,169,279,645,1025,2698,4097,9917,17345,39698,65537,

%T 161395,262145,624004,1089007,2449881,4194305,10097733,16812683,

%U 38754747,69117097,155178266,268435457,629929761,1073741825,2459703907,4400500499,9756737721

%N Number of meanders of length n.

%C A meander is a closed curve drawn by arcs of equal length and central angles of equal magnitude, starting with a positively oriented arc.

%C a(n) = 2^(n-1) + 1 iff n is prime.

%H Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/Meander">Meander</a>.

%F a(n) = Sum_{d|n} A198060(d-1,n/d-1).

%p A199932 := proc(n) local d, k, j, i; add(add(add(add(

%p (-1)^(j+i)*binomial(i,j)*binomial(n/d-1,k)^d*((n/d)/(k+1))^j,

%p i=0..d-1),j=0..d-1),k=0..(n/d-1)),d=numtheory[divisors](n)) end:

%p seq(A199932(i),i=1..34);

%t A198060[m_, n_] := Sum[ Sum[ Sum[(-1)^(j+i)*Binomial[i, j]* Binomial[n, k]^(m+1)*(n+1)^j*(k+1)^(m-j)/(k+1)^m, {i, 0, m}], {j, 0, m}], {k, 0, n}]; a[n_] := Sum[ A198060[d-1, n/d-1], {d, Divisors[n]}]; Table[a[n], {n, 1, 34}] (* _Jean-François Alcover_, Jun 27 2013 *)

%Y Cf. A198060, A200062.

%K nonn

%O 1,2

%A _Peter Luschny_, Nov 20 2011