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A333682
Number of nonnegative lattice paths from (0,0) to (4n+3,0) such that slopes of adjacent steps differ by one, assuming zero slope before and after the paths.
3
1, 3, 16, 119, 1070, 10751, 116287, 1326581, 15756587, 193181910, 2429921124, 31216684816, 408198225495, 5418728779290, 72871393962150, 991102308239835, 13613940451015378, 188650695857473559, 2634681336798911129, 37054660535787380825, 524449965598846642847
OFFSET
0,2
COMMENTS
The maximal height in all paths of length 4n+3 is (n+1)^2 = A000290(n+1).
The maximal area under all paths of length 4n+3 is 2*(n+1)^3 = A033431(n+1).
LINKS
MAPLE
b:= proc(x, y, t) option remember; `if`(x=0, 1, add(`if`(j=t, 0,
b(x-1, y+j, j)), j=max(t-1, -y)..min(x*(x-1)/2-y, t+1)))
end:
a:= n-> b(4*n+3, 0$2):
seq(a(n), n=0..23);
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Apr 01 2020
STATUS
approved