Sequences

Number of rooted compound windmills with n nodes and leaves of 2 colors where any 2 submills extending from the same node are different.

Shifts left 2 places under "CGK" (necklace, element, unlabeled) transform.

Number of series-reduced planted compound windmills with n leaves of 2 colors where any 2 submills extending from the same node are different.

Number of aperiodic necklaces of n beads of 6 colors; dimensions of free Lie algebras.

Number of aperiodic necklaces of n beads of 10 colors.

Number of aperiodic necklaces of n beads of 11 colors.

Number of aperiodic necklaces of n beads of 12 colors.

Number of aperiodic necklaces of n beads of 2 colors, 10 of them black.

Number of aperiodic necklaces of n beads of 2 colors, 11 of them black.

"CHK" (necklace, identity, unlabeled) transform of 1, 2, 3, 4, ...

Number of rooted compound windmills (mobiles) of n nodes with no symmetries.

Number of rooted compound windmills with n nodes and leaves of 2 colors with no symmetries.

Sequence (a(n): n >= 1) that shifts left 2 places under the "CHK" (necklace, identity, unlabeled) transform and has initial terms a(1) = a(2) = 1.

Number of series-reduced planted compound windmills with n leaves of 2 colors with no symmetries.

Number of connected functions of n points with no symmetries.

Functions of n points with no symmetries.

Number of connected functions of n points with no fixed points and with no symmetries.

Number of functions of n points with no fixed points and with no symmetries.

Number of necklaces with n labeled beads of 3 colors.

Number of ways to partition n labeled elements into 6 pie slices.

Number of ways to partition n labeled elements into pie slices each of at least 2 elements.

"CIJ" (necklace, indistinct, labeled) transform of 2,1,1,1...

"CIJ" (necklace, indistinct, labeled) transform of 3,3,3,3...

a(n) = 2^n*(n-1)! for n > 1, a(1) = 1.

Shifts left under "CIJ" (necklace, indistinct, labeled) transform.

Shifts left 2 places under "CIJ" (necklace, indistinct, labeled) transform.

Shifts left 3 places under "CIJ" (necklace, indistinct, labeled) transform.

Number of labeled series-reduced mobiles (circular rooted trees) with n leaves (root has degree 0 or >= 2).

Number of ways to partition n elements into pie slices each with an odd number of elements.

Number of cyclic compositions of n into parts >= 2.

Number of necklaces with 6 black beads and n-6 white beads.

Number of necklaces with 7 black beads and n-7 white beads.

Number of necklaces with 8 black beads and n-8 white beads.

Number of necklaces with 9 black beads and n-9 white beads.

Number of necklaces with 10 black beads and n-10 white beads.

Number of necklaces with 11 black beads and n-11 white beads.

Number of necklaces with 12 black beads and n-12 white beads.

"CIK" (necklace, indistinct, unlabeled) transform of 1,2,3,4,...

"CIK" (necklace, indistinct, unlabeled) transform of 3,5,7...

Number of rooted compound windmills (mobiles) of n nodes.

Number of rooted compound windmills with n nodes and leaves of 2 colors.

Sequence (a(n): n >= 1) that shifts left 2 places under the "CIK" (necklace, indistinct, unlabeled) transform and satisfies a(1) = a(2) = 1.

Number of series-reduced planted compound windmills with n leaves.

Number of series-reduced planted compound windmills with n leaves of 2 colors.

Number of connected functions on n points with a loop of length 9.

Number of connected functions on n points with a loop of length 10.

Number of connected functions on n points with a loop of length 11.

Number of connected functions on n points with a loop of length 12.

"DFJ" (bracelet, size, labeled) transform of 2,2,2,2...

"DFJ" (bracelet, size, labeled) transform of 2,1,1,1...