Sequences Pansy and Peony

Studies of Boolean functions
sequences related to Boolean functions
0 1 2 3 4 5 6 7
Lotus 2 2 10 218 64594 4294642034 18446744047940725978
Pansy (A342286) 2 0 2 8 210 64384 4294577650 18446744043646148328
Peony (A342287) 0 2 0 10 208 64386 4294577648 18446744043646148330

The entries of both sequences differ by 2. Pansy is bigger for even n. (Peony for odd n.)

Both sequences are related to Lotus, the number of all dense BF:     S(n) = Lotus(n−1) − S(n−1)

Pansy a ↦ dense self-reverse Pansy(a) is the number of dense self-reverse BF with arity a.
Peony a ↦ dense self-dual Pansy(a) is the number of dense self-dual BF with arity a.

These are the diagonals of triangles Chestnut and Chinkapin.

This article is issued from Wikiversity. The text is available under Creative Commons Attribution-Share Alike 4.0 unless otherwise noted. Additional terms may apply for the media files.