A148431 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, 1, 0), (0, 1, -1), (0, 1, 0), (1, -1, 1)}.

1, 1, 2, 5, 19, 60, 227, 809, 3310, 12663, 53248, 213217, 918373, 3796553, 16616890, 70310328, 311537659, 1341681580, 6001753284, 26205738839, 118120354572, 521464321540, 2365096085563, 10535212139384, 48029306987720, 215539833379686, 986915535822941, 4456681940039117, 20482312775594355

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A072468 A148430 A062666 * A321006 A320276 A148432

Adjacent sequences: A148428 A148429 A148430 * A148432 A148433 A148434

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved