A374738 Table read by ascending antidiagonals: T(m,n) = number of (n-1)-metered (m,n)-parking functions.
1, 1, 2, 1, 3, 3, 1, 4, 8, 4, 1, 6, 16, 15, 5, 1, 8, 27, 50, 24, 6, 1, 12, 48, 125, 108, 35, 7, 1, 16, 96, 257, 432, 196, 48, 8, 1, 24, 162, 540, 1296, 1029, 320, 63, 9, 1, 32, 288, 1200, 3156, 4802, 2048, 486, 80, 10, 1, 48, 576, 3000, 7734, 16807, 12288, 3645, 700, 99, 11
Offset: 1
Examples
Table begins: 1, 2, 3, 4, 5, 6, 7, ... 1, 3, 8, 15, 24, 35, 48, ... 1, 4, 16, 50, 108, 196, 320, ... 1, 6, 27, 125, 432, 1029, 2048, ... 1, 8, 48, 257, 1296, 4802, 12288, ... 1, 12, 96, 540, 3156, 16807, 65536, ... 1, 16, 162, 1200, 7734, 47442, 262144, ... ...
Links
- Spencer Daugherty, Pamela E. Harris, Ian Klein, and Matt McClinton, Metered Parking Functions, arXiv:2406.12941 [math.CO], 2024.
Formula
T(n+k,n) = Sum_{sigma = (sigma_1, ..., sigma_n) in S_n} (( Product_{i=1..n} L_{i}(sigma))( Product_{j=1..k} sigma_j mod n )), where k>0 and L_{i}(sigma) is the largest index h with i= sigma_N for all N in {i-j, i-j+1, ..., i-1, i}.