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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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Table of n, a(n) for n=1..66. 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. Cf. A001353, A004254, A001109, A004187, A372818, A372821. Sequence in context: A279587 A127952 A171307 * A209693 A154344 A134409 Adjacent sequences: A372814 A372815 A372816 * A372818 A372819 A372820 KEYWORD nonn,tabl AUTHOR Spencer Daugherty, May 13 2024 STATUS approved

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Last modified September 12 15:38 EDT 2024. Contains 375853 sequences. (Running on oeis4.)