A150072 - OEIS

A150072

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

1, 2, 6, 18, 65, 235, 924, 3584, 14685, 59739, 252404, 1057050, 4552029, 19472054, 85142974, 369881012, 1635207275, 7189370970, 32073487208, 142355800384, 639620083601, 2860850548252, 12931842528134, 58210175585589, 264437645539445, 1196711869085656, 5459851377934327, 24821711727873379

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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, j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 1 + 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: A265945 A007454 A305578 * A150073 A150074 A349367

Adjacent sequences: A150069 A150070 A150071 * A150073 A150074 A150075

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved