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A372821
Table read by antidiagonals: T(m,n) = number of (m-2)-metered (m,n)-parking functions
6
0, 1, 0, 0, 4, 0, 0, 4, 9, 0, 0, 0, 21, 16, 0, 0, 0, 27, 56, 25, 0, 0, 0, 0, 163, 115, 36, 0, 0, 0, 0, 257, 483, 204, 49, 0, 0, 0, 0, 0, 1686, 1095, 329, 64, 0, 0, 0, 0, 0, 3156, 5367, 2131, 496, 81, 0, 0, 0, 0, 0, 0, 21858, 13076, 3747, 711, 100, 0, 0, 0, 0, 0, 0, 47442, 73276, 27309, 6123, 980, 121, 0
OFFSET
1,5
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-m+2)^2*(m-1)^(m-3) + Sum_{k=n-m+3...n} binomial(m-2, n-k)*(n-k+1)^(n-k-1)*[binomial(k+1,2)*(n+m+2)*k^(m-n+k-3) + (k*(n-m+1) - binomial(n-m+2,2))*(k-n+m-1)^(k-n+m-3) + Sum_{j=n-m+2} (jk - binomial(j+1,2))*binomial(m-2-n+k, k-1-j)*(n-m+1)*j^(j+m-2-n)*(k-j)^(k-j-2)].
EXAMPLE
Table begins:
0, 0, 0, 0, 0, 0, 0, ...
1, 4, 9, 16, 25, 36, 49, ...
0, 4, 21, 56, 115, 204, 329, ...
0, 0, 27, 163, 483, 1095, 2131, ...
0, 0, 0, 257, 1686, 5367, 13076, ...
0, 0, 0, 0, 3156, 21858, 73276, ...
0, 0, 0, 0, 0, 47442, 341192, ...
...
CROSSREFS
Main diagonal is A328694.
Sequence in context: A308256 A096406 A189885 * A151673 A005397 A259124
KEYWORD
nonn,tabl
AUTHOR
Spencer Daugherty, May 13 2024
STATUS
approved