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A200062 Meanders of length n and central angle < 360 degrees. 3
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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: A226478 A328235 A293129 * A229468 A319039 A107873

Adjacent sequences:  A200059 A200060 A200061 * A200063 A200064 A200065

KEYWORD

nonn

AUTHOR

Peter Luschny, Nov 16 2011

STATUS

approved

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Last modified February 25 08:21 EST 2020. Contains 332221 sequences. (Running on oeis4.)