A148204 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, 0, 0), (-1, 0, 1), (0, 0, 1), (0, 1, -1), (1, -1, 1)}.

1, 1, 2, 4, 12, 35, 113, 375, 1310, 4703, 17330, 65209, 250114, 973787, 3843412, 15348830, 61943321, 252282099, 1036030465, 4286325796, 17852945250, 74812425886, 315247690475, 1335177040541, 5681387342453, 24279598309480, 104174406713499, 448629070128615, 1938691951621376, 8404757306420331

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], 2009.

Maple

Steps:= [[-1, 0, 0], [-1, 0, 1], [0, 0, 1], [0, 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..40], [0, 0, 0]); # Robert Israel, Dec 13 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, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 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: A215953 A209027 A069727 * A151525 A148205 A019447

Adjacent sequences: A148201 A148202 A148203 * A148205 A148206 A148207

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved