A148448 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), (-1, 1, 0), (0, 1, 1), (1, 0, -1)}.

1, 1, 2, 6, 17, 50, 171, 567, 1986, 7141, 25885, 96335, 361948, 1377016, 5303325, 20571802, 80572919, 317654987, 1260703066, 5033962911, 20202671783, 81492060501, 330138308530, 1342982590056, 5483760216426, 22469085384921, 92364016812169, 380813151198233, 1574483590304631, 6526707421820414

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, -1 + j, 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: A025272 A356783 A148447 * A148449 A148450 A153773

Adjacent sequences: A148445 A148446 A148447 * A148449 A148450 A148451

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved