A150419 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), (1, 0, 0), (1, 0, 1), (1, 1, -1)}.

1, 2, 7, 24, 95, 381, 1613, 6932, 30505, 136024, 614390, 2803286, 12898887, 59793748, 278890182, 1307942025, 6162995635, 29161344023, 138493371160, 659897593518, 3153595560519, 15110731364325, 72578237594724, 349358632561298, 1684987109407095, 8141562701614015, 39403909634507164, 190999986880062894

Offset

0,2

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, j, 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: A150416 A150417 A150418 * A150420 A150421 A150422

Adjacent sequences: A150416 A150417 A150418 * A150420 A150421 A150422

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved