A149921 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, 0, -1), (-1, 0, 1), (0, 1, 0), (1, 0, 0)}.

1, 2, 5, 15, 47, 158, 546, 1959, 7186, 26752, 101598, 390218, 1515442, 5942431, 23505016, 93645233, 375351768, 1514057193, 6138079032, 24996491647, 102243003319, 419849010522, 1730025591625, 7151698005385, 29656218739201, 123313206841880, 514038736373565, 2148049283949433, 8996338290624829

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, j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 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: A353028 A149919 A149920 * A149922 A192053 A013560

Adjacent sequences: A149918 A149919 A149920 * A149922 A149923 A149924

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved