A150612 - OEIS

A150612

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

1, 2, 7, 27, 112, 477, 2118, 9510, 43614, 201517, 942815, 4432835, 21013136, 99957322, 478180218, 2293491483, 11045190763, 53298966235, 257981267156, 1250679309301, 6077456225356, 29570250061295, 144141694863179, 703369802279715, 3437330839352784, 16812939983768125, 82336329565180367

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..26.

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[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + 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: A150609 A150610 A150611 * A150613 A150614 A182454

Adjacent sequences: A150609 A150610 A150611 * A150613 A150614 A150615

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved