cp's OEIS Frontend

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

%I A200062 #13 Aug 11 2014 22:45:47
%S A200062 0,1,1,4,1,15,1,41,23,133,1,650,1,1725,961,6930,1,30323,1,99716,40431,
%T A200062 352729,1,1709125,35467,5200315,2008233,20960538,1,93058849,1,
%U A200062 312220259,105533203,1166803129,20194059,5478229800,1,17672631921,5731781295,71539226243,1
%N A200062 Meanders of length n and central angle < 360 degrees.
%C A200062 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 A200062 a(n) = 1 if and only if n is prime.
%H A200062 Peter Luschny, <a href="/A200062/b200062.txt">Table of n, a(n) for n = 1..1000</a>
%H A200062 Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/Meander">Meander</a>.
%F A200062 a(n) = Sum_{d|n} A198060(d-1,n/d-1) - 2^(n-1).
%e A200062 See the link for n = 6,8,9.
%p A200062 A200062 := proc(n) local i;
%p A200062 add(A198060(i-1,n/i-1),i=numtheory[divisors](n)) - 2^(n-1) end: seq(A200062(i),i=1..41);
%t A200062 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 A200062 (PARI)
%o A200062 A200062(n) = { D = divisors(n);
%o A200062 sum(m = 2, #D, d = D[m];
%o A200062    sum(k=0,n/d-1,binomial(n/d-1,k)^d*
%o A200062       sum(j=0,d-1,((n/d)/(k+1))^j*
%o A200062           sum(i=0,d-1,(-1)^(j+i)*binomial(i,j)
%o A200062 ))))}
%Y A200062 Cf. A198060, A199932.
%K A200062 nonn
%O A200062 1,4
%A A200062 _Peter Luschny_, Nov 16 2011