A200062 Meanders of length n and central angle < 360 degrees.

0, 1, 1, 4, 1, 15, 1, 41, 23, 133, 1, 650, 1, 1725, 961, 6930, 1, 30323, 1, 99716, 40431, 352729, 1, 1709125, 35467, 5200315, 2008233, 20960538, 1, 93058849, 1, 312220259, 105533203, 1166803129, 20194059, 5478229800, 1, 17672631921, 5731781295, 71539226243, 1

Offset: 1

Author

Peter Luschny, Nov 16 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) = 1 if and only if n is prime.

Examples

			See the link for n = 6,8,9.
		

Links

• Peter Luschny, Table of n, a(n) for n = 1..1000
• Peter Luschny, Meander.

Crossrefs

Cf. A198060, A199932.

Programs

Maple

A200062 := proc(n) local i;
add(A198060(i-1,n/i-1),i=numtheory[divisors](n)) - 2^(n-1) end: seq(A200062(i),i=1..41);

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]}] - 2^(n-1); Table[a[n], {n, 1, 41}] (* Jean-François Alcover, Jun 27 2013 *)

PARI

A200062(n) = { D = divisors(n);
sum(m = 2, #D, d = D[m];
   sum(k=0,n/d-1,binomial(n/d-1,k)^d*
      sum(j=0,d-1,((n/d)/(k+1))^j*
          sum(i=0,d-1,(-1)^(j+i)*binomial(i,j)
))))}

Formula

a(n) = Sum_{d|n} A198060(d-1,n/d-1) - 2^(n-1).