A149451 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, 0), (0, -1, 1), (0, 1, 1), (1, -1, 1), (1, 0, -1)}.

1, 1, 4, 13, 49, 186, 751, 3098, 13036, 55559, 239741, 1045683, 4598980, 20368516, 90733028, 406321477, 1827966938, 8257125139, 37430455001, 170216663711, 776294282712, 3549614438904, 16269011949135, 74726516665971, 343909812071896, 1585633519847133, 7323006530686385, 33872716318708966

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[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A338862 A097948 A096971 * A149452 A140660 A149453

Adjacent sequences: A149448 A149449 A149450 * A149452 A149453 A149454

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved