OFFSET
1,2
COMMENTS
This sequence enumerates parking functions with n cars and n parking spots with lucky k-th spot (where a lucky spot is one which is parked in by a car which prefers that spot).
EXAMPLE
Triangle begins:
1;
3, 2;
16, 11, 9;
125, 87, 74, 64;
1296, 908, 783, 708, 625;
16807, 11824, 10266, 9421, 8733, 7776;
...
For clarity, we write parentheses around parking functions. For n = 3 and k = n-1 = 2, the T(3,2) = 11 solutions are the parking functions of length 3 with a lucky second spot: (1,2,1),(1,2,2),(1,2,3),(1,3,2),(2,1,1),(2,1,2),(2,1,3),(2,2,1),(2,3,1),(3,1,2),(3,2,1). There are 5 parking functions of length 3 which do not have a lucky second spot: (1,1,1),(1,1,2),(1,1,3),(1,3,1),(3,1,1). For all of these, the car which parks in the second spot did not prefer the second spot; these parking functions do not contribute to our count.
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Kimberly P. Hadaway, Jul 18 2024
STATUS
approved