A149846 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), (0, 1, 0), (1, 0, 0), (1, 1, -1)}.

1, 2, 4, 12, 38, 118, 424, 1544, 5668, 22186, 86962, 347260, 1426428, 5869950, 24589692, 104252754, 444133962, 1916625390, 8318626668, 36335194794, 159998657938, 707382646426, 3146397539508, 14064764511358, 63107673236226, 284521869849658, 1287188819030996, 5843899644335638, 26625968697335426

Offset

0,2

Links

Table of n, a(n) for n=0..28.

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, k, -1 + n] + aux[i, -1 + j, 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: A149844 A149845 A217616 * A341240 A108532 A213058

Adjacent sequences: A149843 A149844 A149845 * A149847 A149848 A149849

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved