A149057 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 0), (-1, 1, 1), (0, 1, 1), (1, -1, 1), (1, 1, -1)}.

1, 1, 3, 10, 41, 158, 703, 2966, 13622, 60295, 282385, 1285337, 6097884, 28283284, 135373026, 636175260, 3064466767, 14540133618, 70377730620, 336373997612, 1634218219670, 7855462500604, 38278123228839, 184836490256889, 902854275332470, 4375843959459194, 21417210557620449, 104120226745428208

Offset

0,3

Links

Robert Israel, Table of n, a(n) for n = 0..200

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

Maple

Steps:= [[-1, -1, 0], [-1, 1, 1], [0, 1, 1], [1, -1, 1], [1, 1, -1] ]:
f:= proc(n, p) option remember;
  if n <= min(p) then return 5^n fi;
  add(procname(n-1, t), t=remove(has, map(`+`, Steps, p), -1));
end proc:
map(f, [$0..30], [0, 0, 0]); # Robert Israel, Dec 12 2019

Mathematica

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A213108 A163843 A149056 * A149058 A151078 A151079

Adjacent sequences: A149054 A149055 A149056 * A149058 A149059 A149060

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved