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A374738
Table read by ascending antidiagonals: T(m,n) = number of (n-1)-metered (m,n)-parking functions.
0
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
1,3
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<h for which sigma_i >= sigma_N for all N in {i-j, i-j+1, ..., i-1, i}.
EXAMPLE
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, ...
...
CROSSREFS
The n=m+1 diagonal is A007334.
Sequence in context: A208597 A179943 A089944 * A180165 A358349 A376479
KEYWORD
nonn,tabl
AUTHOR
Spencer Daugherty, Jul 18 2024
STATUS
approved