A148792 - OEIS

A148792

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

1, 1, 3, 8, 25, 77, 258, 859, 2951, 10083, 35463, 124321, 440777, 1564412, 5613436, 20126465, 72600868, 262274477, 952091511, 3458207202, 12605564464, 46002034866, 168328851812, 616532841066, 2262999692234, 8314445493372, 30601371089696, 112732187972575, 415875293473076, 1535492331618463

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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, -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: A088327 A148790 A148791 * A007563 A050383 A060404

Adjacent sequences: A148789 A148790 A148791 * A148793 A148794 A148795

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved