OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..50
FORMULA
a(n) = Sum_{d|4} phi(4/d)*(n*d)!/(d!^n*n*4) if n>0 and a(0) = 1.
For n > 0, a(n) = (4*n)!/(4*n*24^n) + (n-1)!/2 + (2*n-1)!/2^(n+1). - Vaclav Kotesovec, Aug 23 2015
EXAMPLE
a(0) = 1: the empty necklace.
a(1) = 1: {0000}.
a(2) = 10: {00001111, 00010111, 00100111, 01000111, 00011011, 00110011, 00101011, 01010011, 01001011, 01010101}.
MAPLE
with(numtheory);
a:= n-> `if`(n=0, 1, add(phi(4/d) *(n*d)!/(d!^n *4*n), d={1, 2, 4})):
seq(a(n), n=0..15);
MATHEMATICA
Flatten[{1, Table[(4*n)!/(4*n*24^n) + (n-1)!/2 + (2*n-1)!/2^(n+1), {n, 1, 15}]}] (* Vaclav Kotesovec, Aug 23 2015 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Feb 24 2012
STATUS
approved