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A372817
Table read by antidiagonals: T(m,n) = number of 1-metered (m,n)-parking functions.
4
1, 0, 2, 0, 3, 3, 0, 4, 8, 4, 0, 6, 21, 15, 5, 0, 8, 55, 56, 24, 6, 0, 12, 145, 209, 115, 35, 7, 0, 16, 380, 780, 551, 204, 48, 8, 0, 24, 1000, 2912, 2640, 1189, 329, 63, 9, 0, 32, 2625, 10868, 12649, 6930, 2255, 496, 80, 10, 0, 48, 6900, 40569, 60606, 40391, 15456, 3905, 711, 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(m,n) = (n*(n+sqrt(n^2 - 4))-2)/(n*(n+sqrt(n^2 - 4))-4)*((n+sqrt(n^2-4))/2)^m + (n*(n-sqrt(n^2 - 4))-2)/(n*(n-sqrt(n^2 - 4))-4)*((n-sqrt(n^2-4))/2)^m.
T(m,n) = n*T(m-1,n) - T(m-2,n) with T(0,n) = 1.
EXAMPLE
For T(3,2) the 1-metered (3,2)-parking functions are 111, 121, 211, 212.
Table begins:
1, 2, 3, 4, 5, 6, 7, ...
0, 3, 8, 15, 24, 35, 48, ...
0, 4, 21, 56, 115, 204, 329, ...
0, 6, 55, 209, 551, 1189, 2255, ...
0, 8, 145, 780, 2640, 6930, 15456, ...
0, 12, 380, 2912, 12649, 40391, 105937, ...
0, 16, 1000, 10868, 60606, 235416, 726103, ...
...
CROSSREFS
Main diagonal is A097690 and first row of A372816.
First, second, and third diagonals above main are A097691, A342167, A342168.
Second column A029744. Second row A005563. Third row A242135.
Sequence in context: A279587 A127952 A171307 * A209693 A154344 A134409
KEYWORD
nonn,tabl
AUTHOR
Spencer Daugherty, May 13 2024
STATUS
approved