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

Author

Peter Luschny, Nov 20 2011

Keywords

• nonn
• tabf

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.

Examples

			[ 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
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..482
• Peter Luschny, Meander.

Crossrefs

Cf. A198060, A199932, A200062.

Programs

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 *)

Formula

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