A149570 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, 0), (1, -1, 1), (1, 1, 1)}

1, 1, 5, 13, 63, 201, 991, 3543, 17589, 66675, 331981, 1310121, 6533329, 26526137, 132398363, 548964603, 2741549255, 11553795573, 57721223997, 246430668963, 1231434003299, 5313224430041, 26554997020499, 115586008363819, 577754385702581, 2533497279476529, 12664663772458771, 55888692416822733

Offset

0,3

Links

Robert Israel, Table of n, a(n) for n = 0..182

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

Maple

Steps:= [[-1, -1, 1], [-1, 1, -1], [1, -1, 0], [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..40], [0, 0, 0]); # Robert Israel, Jul 09 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[-1 + i, 1 + j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, 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: A051902 A269514 A149569 * A149571 A149572 A149573

Adjacent sequences: A149567 A149568 A149569 * A149571 A149572 A149573

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved