A149366 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, 1), (0, 0, -1), (0, 1, -1), (1, 0, 1)}.

1, 1, 4, 12, 45, 147, 630, 2379, 10058, 39493, 174771, 722360, 3188845, 13422230, 60590448, 261827778, 1181161187, 5155905071, 23569271399, 104520154563, 477730909858, 2131929784360, 9829716330049, 44325686668781, 204387251744233, 925589306495805, 4294222692273509, 19589722213545972

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[i, j, 1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A028407 A105344 A074035 * A370540 A149367 A149368

Adjacent sequences: A149363 A149364 A149365 * A149367 A149368 A149369

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved