This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A372817 #32 Jul 09 2024 20:43:39 %S A372817 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 A372817 0,16,380,780,551,204,48,8,0,24,1000,2912,2640,1189,329,63,9,0,32, %U A372817 2625,10868,12649,6930,2255,496,80,10,0,48,6900,40569,60606,40391,15456,3905,711,99,11 %N A372817 Table read by antidiagonals: T(m,n) = number of 1-metered (m,n)-parking functions. %H A372817 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 A372817 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 A372817 T(m,n) = n*T(m-1,n) - T(m-2,n) with T(0,n) = 1. %e A372817 For T(3,2) the 1-metered (3,2)-parking functions are 111, 121, 211, 212. %e A372817 Table begins: %e A372817 1, 2, 3, 4, 5, 6, 7, ... %e A372817 0, 3, 8, 15, 24, 35, 48, ... %e A372817 0, 4, 21, 56, 115, 204, 329, ... %e A372817 0, 6, 55, 209, 551, 1189, 2255, ... %e A372817 0, 8, 145, 780, 2640, 6930, 15456, ... %e A372817 0, 12, 380, 2912, 12649, 40391, 105937, ... %e A372817 0, 16, 1000, 10868, 60606, 235416, 726103, ... %e A372817 ... %Y A372817 Main diagonal is A097690 and first row of A372816. %Y A372817 First, second, and third diagonals above main are A097691, A342167, A342168. %Y A372817 Second column A029744. Second row A005563. Third row A242135. %Y A372817 Cf. A001353, A004254, A001109, A004187, A372818, A372821. %K A372817 nonn,tabl %O A372817 1,3 %A A372817 _Spencer Daugherty_, May 13 2024