oeis-function-identities

This is a collection of sage notebooks used for investigating some sequences in oeis.

All of the sequences count ordered pairs of functions from [n]->[n] that satisfy certain identities.

Pseudoinverse

• A239768 fgf = f
• A277337 fgf = f and gfg = g
• A275025 fgfg = fg
• tbd fgfg=fg and gfgf=gf

Generalized tree polynomials

• A239761 fg = f
• A239777 fgg = f
• A245912 fg^3 = f
• A245913 fg^4 = f
• A245914 fg^5 = f
• A245915 fg^6 = f
• A245916 fg^7 = f
• A245917 fg^8 = f
• A245918 fg^9 = f
• A245919 fg^10 = f
• A245910 The two dimensional table containing the counts of fg^k=f

Cyclic Count

+A239760 ffg = f