A148370 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, 0, 1), (-1, 1, -1), (0, 1, 1), (1, 0, -1)}.

1, 1, 2, 5, 16, 42, 147, 454, 1628, 5425, 20178, 70153, 268235, 963094, 3750168, 13820410, 54545612, 205188861, 818752204, 3130596415, 12607433542, 48850200688, 198265158766, 776800033465, 3173598172091, 12552548689917, 51573263660315, 205664370031343, 849144348277944, 3410421662866518

Offset

0,3

Links

Robert Israel, Table of n, a(n) for n = 0..210

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

Maple

Steps:= [[-1, -1, 1], [-1, 0, 1], [-1, 1, -1], [0, 1, 1], [1, 0, -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..40], [0, 0, 0]); # Robert Israel, Jul 11 2018

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, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A102866 A148368 A148369 * A148371 A148372 A148373

Adjacent sequences: A148367 A148368 A148369 * A148371 A148372 A148373

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved