A148184 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), (-1, 1, 1), (0, 1, 0), (1, -1, 0)}.

1, 1, 2, 4, 12, 29, 94, 268, 922, 2875, 10299, 33924, 125228, 430637, 1624161, 5760773, 22105631, 80409248, 312835080, 1160261458, 4565944319, 17217530128, 68405677784, 261423539372, 1047137870008, 4049016463614, 16332743675511, 63775015226718, 258831511396703, 1019535164794358, 4160163682555691

Offset

0,3

Links

Robert Israel, Table of n, a(n) for n = 0..220

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

Maple

Steps:= [[-1, -1, 0], [-1, 1, -1], [-1, 1, 1], [0, 1, 0], [1, -1, 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..30], [0, 0, 0]); # Robert Israel, Nov 22 2020

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, k, -1 + n] + aux[i, -1 + j, 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, 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: A331687 A148182 A148183 * A148185 A215871 A130135

Adjacent sequences: A148181 A148182 A148183 * A148185 A148186 A148187

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved