A150716 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, 1), (1, 0, -1), (1, 0, 1), (1, 1, 1)}.

1, 2, 8, 28, 112, 424, 1696, 6608, 26432, 104272, 417088, 1655376, 6621504, 26364496, 105457984, 420652976, 1682611904, 6718702608, 26874810432, 107379799984, 429519199936, 1716841932112, 6867367728448, 27456530556080, 109826122224320, 439167350629520, 1756669402518080, 7025210349385200

Offset

0,2

Links

Table of n, a(n) for n=0..27.

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

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, j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, 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: A150715 A356933 A026528 * A151299 A150717 A150718

Adjacent sequences: A150713 A150714 A150715 * A150717 A150718 A150719

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved