A200062 - OEIS

%I #13 Aug 11 2014 22:45:47

%S 0,1,1,4,1,15,1,41,23,133,1,650,1,1725,961,6930,1,30323,1,99716,40431,

%T 352729,1,1709125,35467,5200315,2008233,20960538,1,93058849,1,

%U 312220259,105533203,1166803129,20194059,5478229800,1,17672631921,5731781295,71539226243,1

%N Meanders of length n and central angle < 360 degrees.

%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) = 1 if and only if n is prime.

%H Peter Luschny, <a href="/A200062/b200062.txt">Table of n, a(n) for n = 1..1000</a>

%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) - 2^(n-1).

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

%p A200062 := proc(n) local i;

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

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

%o (PARI)

%o A200062(n) = { D = divisors(n);

%o sum(m = 2, #D, d = D[m];

%o    sum(k=0,n/d-1,binomial(n/d-1,k)^d*

%o       sum(j=0,d-1,((n/d)/(k+1))^j*

%o           sum(i=0,d-1,(-1)^(j+i)*binomial(i,j)

%o ))))}

%Y Cf. A198060, A199932.

%K nonn

%O 1,4

%A _Peter Luschny_, Nov 16 2011