A341300 a(n) = n! + (n-1)! + (n-2)! + (n-3)! + n - 3.

10, 34, 154, 873, 5908, 46205, 408966, 4037047, 43948808, 522910089, 6749568010, 93924230411, 1401558681612, 22323869568013, 378005070643214, 6780291598080015, 128424084332544016, 2561305169719296017, 53651891654000640018, 1177646217057902592019

Offset: 3

Author

N. J. A. Sloane, Feb 13 2021

Keywords

• nonn

Comments

a(n) is an upper bound for the length of a minimal superpermutation on n symbols (see links). A lower bound is given by A376269(n). - Paolo Xausa, Sep 27 2024

Links

• Michael De Vlieger, Table of n, a(n) for n = 3..449
• Michael Engen and Vincent Vatter, Containing all permutations, Amer. Math. Monthly, 128 (2021), 4-24; arXiv preprint, arXiv:1810.08252 [math.CO], 2018-2020.
• Wikipedia, Superpermutation.

Crossrefs

Cf. A180632, A332089, A376269.

Programs

Mathematica

Array[Total[(# - Range[0, 3])!] + # - 3 &, 20, 3] (* Michael De Vlieger, Apr 07 2021 *)

Python

from sympy import factorial
def A341300(n): return (n**2*(n-2)+1)*factorial(n-3)+n-3 # Chai Wah Wu, Sep 20 2024

Formula

a(n) = (n-3)!*(n^2*(n-2) + 1) + n - 3. - Chai Wah Wu, Sep 20 2024