A149899 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, 0), (0, 1, 0), (0, 1, 1), (1, -1, -1)}.

1, 2, 5, 14, 47, 159, 565, 2063, 7865, 30157, 118017, 469064, 1892519, 7681288, 31525714, 130593424, 544754098, 2284273316, 9645909083, 40963272701, 174700576880, 748259285162, 3219949393396, 13907429430622, 60257237322969, 261964987031169, 1142598100016005, 4996769804097317

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[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, j, 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: A231211 A006216 A148337 * A149900 A149901 A149902

Adjacent sequences: A149896 A149897 A149898 * A149900 A149901 A149902

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved