A199932 Number of meanders of length n.

1, 3, 5, 12, 17, 47, 65, 169, 279, 645, 1025, 2698, 4097, 9917, 17345, 39698, 65537, 161395, 262145, 624004, 1089007, 2449881, 4194305, 10097733, 16812683, 38754747, 69117097, 155178266, 268435457, 629929761, 1073741825, 2459703907, 4400500499, 9756737721

Offset: 1

Author

Peter Luschny, Nov 20 2011

Keywords

• nonn

Comments

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

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

Links

• Peter Luschny, Meander.

Crossrefs

Cf. A198060, A200062.

Programs

Maple

A199932 := proc(n) local d, k, j, i; add(add(add(add(
(-1)^(j+i)*binomial(i,j)*binomial(n/d-1,k)^d*((n/d)/(k+1))^j,
i=0..d-1),j=0..d-1),k=0..(n/d-1)),d=numtheory[divisors](n)) end:
seq(A199932(i),i=1..34);

Mathematica

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 *)

Formula

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