A148240 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, -1), (-1, -1, 1), (-1, 1, 1), (0, 1, -1), (1, 0, 0)}.

1, 1, 2, 4, 13, 36, 110, 367, 1243, 4266, 14979, 54636, 199011, 734030, 2756839, 10450319, 39836796, 153059496, 593960500, 2316916479, 9077686257, 35778018898, 141845770750, 564450779427, 2253100544758, 9036652220948, 36388658308498, 146848107101360, 594357667427186, 2414872472739607

Offset

0,3

Links

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

Alin Bostan and Manuel Kauers, Automatic Classification of Restricted Lattice Walks, arXiv:0811.2899 [math.CO], 2008-2009.

Maple

Steps:= [[-1, -1, -1], [-1, -1, 1], [-1, 1, 1], [0, 1, -1], [1, 0, 0]]:
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..40], [0, 0, 0]); # Robert Israel, Apr 11 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, j, 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, -1 + k, -1 + n] + aux[1 + i, 1 + j, 1 + 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: A148238 A278281 A148239 * A151354 A148241 A148242

Adjacent sequences: A148237 A148238 A148239 * A148241 A148242 A148243

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved