A150330 - OEIS

A150330

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

1, 2, 7, 22, 88, 325, 1393, 5608, 24956, 105724, 482023, 2111713, 9789238, 43910561, 206007470, 940232408, 4451025298, 20584939237, 98131246779, 458551690091, 2198147038752, 10356948398945, 49871960706234, 236570491322896, 1143403833885538, 5454155291768239, 26443461240591709, 126729564192829473

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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, k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[-1 + i, 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: A150328 A150329 A323681 * A150331 A150332 A150333

Adjacent sequences: A150327 A150328 A150329 * A150331 A150332 A150333

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved