A208188 Number of distinct n-colored necklaces with 7 beads per color.

1, 1, 246, 19003476, 16875655269948, 90784545100668913392, 2041012695880532470281654960, 150277870737901828652705825755721760, 30495546426686489361833408314854897254404320, 14997592385781765578538605874290442908069285068834560

Offset: 0

Author

Alois P. Heinz, Feb 24 2012

Keywords

• nonn

Examples

			a(0) =   1: the empty necklace.
a(1) =   1: {0000000}.
a(2) = 246: {00000001111111, ..., 01010101010101}.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..35

Crossrefs

Row n=7 of A208183.

Cf. A000010, A000142.

Programs

Maple

with(numtheory);
a:= n-> `if`(n=0, 1, add(phi(7/d) *(n*d)!/(d!^n *7*n), d={1, 7})):
seq(a(n), n=0..12);

Formula

a(n) = Sum_{d|7} phi(7/d)*(n*d)!/(d!^n*n*7) if n>0 and a(0) = 1.