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A335588 Number of n-step n-dimensional nonnegative lattice walks starting at the origin and using steps that increment all components or decrement one component by 1. 2
1, 1, 3, 13, 81, 686, 7525, 102173, 1655241, 31119382, 665254791, 15927737772, 422179410829, 12275253219828, 388591800808471, 13309116622983421, 490515662121994785, 19362705183912628838, 815258217524407553989, 36479395828632610279316, 1729012534789121191076601 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..65 (terms 0..55 from Alois P. Heinz)

FORMULA

a(n) = A335570(n,n).

a(n) == 1 (mod n) for n >= 2.

EXAMPLE

a(2) = 3: [(0,0),(1,1),(2,2)], [(0,0),(1,1),(0,1)], [(0,0),(1,1),(1,0)].

MAPLE

b:= proc(n, l) option remember; `if`(n=0, 1, b(n-1, map(x-> x+1, l))+add(

     `if`(l[i]>0, b(n-1, sort(subsop(i=l[i]-1, l))), 0), i=1..nops(l)))

    end:

a:= n-> b(n, [0$n]):

seq(a(n), n=0..23);

MATHEMATICA

b[n_, l_] := b[n, l] = If[n == 0, 1, b[n - 1, l + 1] + Sum[If[l[[i]] > 0, b[n - 1, Sort[ReplacePart[l, i -> l[[i]] - 1]]], 0], {i, 1, Length[l]}]];

a[n_] := b[n, Table[0, {n}]];

a /@ Range[0, 23] (* Jean-François Alcover, Jan 29 2021, after Alois P. Heinz *)

CROSSREFS

Main diagonal of A335570.

Sequence in context: A160882 A135921 A005923 * A089461 A000684 A222272

Adjacent sequences:  A335585 A335586 A335587 * A335589 A335590 A335591

KEYWORD

nonn,walk

AUTHOR

Alois P. Heinz, Jan 26 2021

STATUS

approved

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Last modified December 1 16:44 EST 2021. Contains 349430 sequences. (Running on oeis4.)