A200583 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.

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

Offset

1,2

Comments

A meander is a closed curve drawn by arcs of equal length and central angle of equal magnitude, starting with a positively oriented arc.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..482

Peter Luschny, Meander.

Formula

T(n,k) = A198060(d-1,n/d-1) where d is the k-th divisor of n (the divisors in natural order).

Example

[ 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

Maple

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);

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}]; 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 *)

Crossrefs

Cf. A198060, A199932, A200062.

Sequence in context: A307683 A248058 A072345 * A366842 A115120 A147373

Adjacent sequences: A200580 A200581 A200582 * A200584 A200585 A200586

Keyword

nonn,tabf

Author

Peter Luschny, Nov 20 2011

Status

approved