A322782 Number of lattice paths from {2}^n to {0}^n using steps that decrement one component by 1 such that for each point (p_1,p_2,...,p_n) we have abs(p_{i}-p_{i+1}) <= 1 and abs(p_{1}-p_{n}) <= 1.
1, 1, 4, 36, 720, 23400, 1123200, 74440800, 6509318400, 725829724800, 100511918784000, 16922530756454400, 3404178048774758400, 806369627582929612800, 222159405758654317363200, 70435689828806256514560000, 25463217531292911649057996800, 10411540182139235537714555289600
Offset: 0
Programs
-
Maple
b:= proc(l) option remember; (n-> `if`(n<2 or max(l[])=0, 1, add(`if`(l[i]=0 or 1 -
Mathematica
b[l_] := b[l] = With[{n = Length[l]}, If[n < 2 || Max[l ] == 0, 1, Sum[If[ l[[i]] == 0 || 1 < Abs[l[[If[i == 1, 0, i] - 1]] - l[[i]] + 1] || 1 < Abs[l[[If[i == n, 0, i] + 1]] - l[[i]] + 1], 0, b[ReplacePart[l, i -> l[[i]] - 1]]], {i, n}]]]; a[n_] := b[Table[2, {n}]]; a /@ Range[0, 12] (* Jean-François Alcover, May 13 2020, after Alois P. Heinz *)
Formula
a(n) = n * A318191(2,n) for n > 0. - Alois P. Heinz, Jan 09 2019
Extensions
More terms from Alois P. Heinz, Dec 30 2018