A149325 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, 0, 0), (-1, 0, 1), (0, 1, -1), (1, 0, 1)}.

1, 1, 4, 12, 38, 142, 517, 1951, 7513, 29512, 117109, 467749, 1895238, 7712705, 31588149, 130133561, 538672492, 2239216530, 9339478963, 39101989768, 164180421600, 691191046990, 2917387518861, 12341734663057, 52320417953755, 222221908195725, 945574242636011, 4030163887084767

Offset

0,3

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, j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, j, 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: A006192 A354341 A149324 * A149326 A149327 A308446

Adjacent sequences: A149322 A149323 A149324 * A149326 A149327 A149328

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved