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%I #32 Jul 09 2024 20:43:39
%S 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,
%T 0,16,380,780,551,204,48,8,0,24,1000,2912,2640,1189,329,63,9,0,32,
%U 2625,10868,12649,6930,2255,496,80,10,0,48,6900,40569,60606,40391,15456,3905,711,99,11
%N Table read by antidiagonals: T(m,n) = number of 1-metered (m,n)-parking functions.
%H Spencer Daugherty, Pamela E. Harris, Ian Klein, and Matt McClinton, <a href="https://arxiv.org/abs/2406.12941">Metered Parking Functions</a>, arXiv:2406.12941 [math.CO], 2024.
%F 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.
%F T(m,n) = n*T(m-1,n) - T(m-2,n) with T(0,n) = 1.
%e For T(3,2) the 1-metered (3,2)-parking functions are 111, 121, 211, 212.
%e Table begins:
%e 1, 2, 3, 4, 5, 6, 7, ...
%e 0, 3, 8, 15, 24, 35, 48, ...
%e 0, 4, 21, 56, 115, 204, 329, ...
%e 0, 6, 55, 209, 551, 1189, 2255, ...
%e 0, 8, 145, 780, 2640, 6930, 15456, ...
%e 0, 12, 380, 2912, 12649, 40391, 105937, ...
%e 0, 16, 1000, 10868, 60606, 235416, 726103, ...
%e ...
%Y Main diagonal is A097690 and first row of A372816.
%Y First, second, and third diagonals above main are A097691, A342167, A342168.
%Y Second column A029744. Second row A005563. Third row A242135.
%Y Cf. A001353, A004254, A001109, A004187, A372818, A372821.
%K nonn,tabl
%O 1,3
%A _Spencer Daugherty_, May 13 2024