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

1,4

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.

Links

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

Peter Luschny, Meander.

Formula

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

Example

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

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 *)

Prog

(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)
))))}

Crossrefs

Cf. A198060, A199932.

Sequence in context: A349124 A328235 A293129 * A338832 A229468 A319039

Adjacent sequences: A200059 A200060 A200061 * A200063 A200064 A200065

Keyword

nonn

Author

Peter Luschny, Nov 16 2011

Status

approved