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.
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