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

Author

Spencer Daugherty, Jul 18 2024

Keywords

• nonn
• tabl

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.

Crossrefs

The n=m+1 diagonal is A007334.

Cf. A372817, A372818, A372819, A372820, A372821.

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}.