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A199932 Meanders of length n. 3
1, 3, 5, 12, 17, 47, 65, 169, 279, 645, 1025, 2698, 4097, 9917, 17345, 39698, 65537, 161395, 262145, 624004, 1089007, 2449881, 4194305, 10097733, 16812683, 38754747, 69117097, 155178266, 268435457, 629929761, 1073741825, 2459703907, 4400500499, 9756737721 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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) = 2^(n-1) + 1 iff n is prime.

LINKS

Table of n, a(n) for n=1..34.

Peter Luschny, Meander.

FORMULA

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

MAPLE

A199932 := proc(n) local d, k, j, i; add(add(add(add(

(-1)^(j+i)*binomial(i, j)*binomial(n/d-1, k)^d*((n/d)/(k+1))^j,

i=0..d-1), j=0..d-1), k=0..(n/d-1)), d=numtheory[divisors](n)) end:

seq(A199932(i), i=1..34);

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]}]; Table[a[n], {n, 1, 34}] (* Jean-Fran├žois Alcover, Jun 27 2013 *)

CROSSREFS

Cf. A198060, A200062.

Sequence in context: A299490 A126471 A317100 * A305552 A226652 A024696

Adjacent sequences:  A199929 A199930 A199931 * A199933 A199934 A199935

KEYWORD

nonn

AUTHOR

Peter Luschny, Nov 20 2011

STATUS

approved

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Last modified November 19 08:44 EST 2019. Contains 329318 sequences. (Running on oeis4.)