A309331 Expansion of (x+x^3+x^5)/(1-x-3*x^3-x^5).

0, 1, 1, 2, 5, 9, 16, 32, 61, 114, 219, 418, 792, 1510, 2878, 5473, 10421, 19847, 37776, 71917, 136931, 260680, 496278, 944847, 1798804, 3424569, 6519790, 12412480, 23631034, 44989208, 85651217, 163064109, 310444213, 591028898, 1125210433

Offset: 0

Author

Colin Defant, Jul 23 2019

Keywords

• easy
• nonn

Comments

a(n) is the number of 231-avoiding permutations of length n that have order 1 or 3.

Links

• Amanda Burcroff and Colin Defant, Pattern-Avoiding Permutation Powers, arXiv:1907.09451 [math.CO], 2019.
• Index entries for linear recurrences with constant coefficients, signature (1,0,3,0,1).

Formula

G.f.: (1-x+x^2)*(1+x+x^2)/(1-x-3*x^3-x^5).