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A200583
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Table read by rows, n >= 1, 1 <= k <= card(divisors(n)), T(n,k) meanders of length n and central angle of 360/d degrees, d the k-th divisor of n.
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1
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1, 2, 1, 4, 1, 8, 3, 1, 16, 1, 32, 10, 4, 1, 64, 1, 128, 35, 5, 1, 256, 22, 1, 512, 126, 6, 1, 1024, 1, 2048, 462, 134, 46, 7, 1, 4096, 1, 8192, 1716, 8, 1, 16384, 866, 94, 1, 32768, 6435, 485, 9, 1, 65536, 1, 131072, 24310, 5812, 190, 10, 1, 262144, 1, 524288
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history;
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OFFSET
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1,2
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COMMENTS
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A meander is a closed curve drawn by arcs of equal length and central angle of equal magnitude, starting with a positively oriented arc.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..482
Peter Luschny, Meander.
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FORMULA
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T(n,k) = A198060(d-1,n/d-1) where d is the k-th divisor of n (the divisors in natural order).
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EXAMPLE
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[ 1] 1
[ 2] 2, 1
[ 3] 4, 1
[ 4] 8, 3, 1
[ 5] 16, 1
[ 6] 32, 10, 4, 1
[ 7] 64, 1
[ 8] 128, 35, 5, 1
[ 9] 256, 22, 1
[10] 512, 126, 6, 1
[11] 1024, 1
[12] 2048, 462, 134, 46, 7, 1
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MAPLE
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A200583_row := proc(n) local i;
seq(A198060(i-1, n/i-1), i=numtheory[divisors](n)) end:
seq(print(A200583_row(i)), i=1..12);
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MATHEMATICA
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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}]; row[n_] := Table[A198060[d-1, n/d-1], {d, Divisors[n]}]; Table[row[n], {n, 1, 20}] // Flatten (* Jean-François Alcover, Feb 25 2014, after Maple *)
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CROSSREFS
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Cf. A198060, A199932, A200062.
Sequence in context: A307683 A248058 A072345 * A115120 A147373 A147441
Adjacent sequences: A200580 A200581 A200582 * A200584 A200585 A200586
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KEYWORD
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nonn,tabf
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AUTHOR
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Peter Luschny, Nov 20 2011
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STATUS
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approved
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