OFFSET
2,1
COMMENTS
a(n) is a lower bound for the length of every superpermutation on n symbols (see links). An upper bound for the length of a minimal superpermutation is given by A341300(n).
LINKS
Paolo Xausa, Table of n, a(n) for n = 2..400
Anonymous 4chan poster, Robin Houston, Jay Pantone, and Vince Vatter, A lower bound on the length of the shortest superpattern, 2018.
Michael Engen and Vincent Vatter, Containing All Permutations, The American Mathematical Monthly, 128 (1), 2021, pp. 4-24 (preprint version).
James Grime and Brady Haran, Superpermutations, Numberphile video, 2018.
Wikipedia, Superpermutation.
FORMULA
a(n) = A054119(n) + n - 3.
E.g.f.: (3 - x - x^2 - exp(x)*(3 - 4*x + x^2) - (1 - x)*x*log(1 - x))/(1 - x). - Stefano Spezia, Sep 18 2024
a(n) = (n-2)!*n^2 + n - 3. - Chai Wah Wu, Sep 20 2024
D-finite with recurrence (-n+1)*a(n) +(n-2)*(n+2)*a(n-1) -(n-1)*(n-3)*a(n-2) -(4*n-7)*(n-4)=0. - R. J. Mathar, Sep 23 2024
MATHEMATICA
Table[n^2 * (n - 2)! + n - 3, {n, 2, 25}]
PROG
(Python)
from sympy import factorial
def A376269(n): return n**2*factorial(n-2)+n-3 # Chai Wah Wu, Sep 20 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paolo Xausa, Sep 18 2024
STATUS
approved