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

1,2

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

Table of n, a(n) for n=1..34.

Peter Luschny, Meander.

Formula

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

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 *)

Crossrefs

Cf. A198060, A200062.

Sequence in context: A361274 A126471 A317100 * A305552 A226652 A024696

Adjacent sequences: A199929 A199930 A199931 * A199933 A199934 A199935

Keyword

nonn

Author

Peter Luschny, Nov 20 2011

Status

approved