A072506 Triangle giving T(n,m) = number of necklaces of two colors with 2n beads of which m=1..n are black.

1, 1, 2, 1, 3, 4, 1, 4, 7, 10, 1, 5, 12, 22, 26, 1, 6, 19, 43, 66, 80, 1, 7, 26, 73, 143, 217, 246, 1, 8, 35, 116, 273, 504, 715, 810, 1, 9, 46, 172, 476, 1038, 1768, 2438, 2704, 1, 10, 57, 245, 776, 1944, 3876, 6310, 8398, 9252, 1, 11, 70, 335, 1197, 3399, 7752

Offset

1,3

Comments

Left half of even rows of triangle A047996 (with the leftmost edge discarded).

Links

Table of n, a(n) for n=1..62.

Formula

(1/(2n)) Sum_{d |(2n, m)} phi(d)*binomial(2n/d, m/d)

Mathematica

Table[(Plus@@(EulerPhi[ # ]Binomial[2n/#, m/# ] &)/@Intersection[Divisors[2n], Divisors[m]])/(2n), {n, 13}, {m, n}]

Crossrefs

Penultimate entries give binary necklaces of n-1 black beads and n+1 white beads, presumably A007595, antepenultimate entries give binary necklaces of n-2 black beads and n+2 white beads, presumably A003444.

Cf. A047996, A003444.

Sequence in context: A076832 A078925 A361042 * A188236 A181851 A210231

Adjacent sequences: A072503 A072504 A072505 * A072507 A072508 A072509

Keyword

nonn,tabl

Author

Wouter Meeussen, Aug 03 2002

Status

approved