A150398 - OEIS

A150398

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

1, 2, 7, 24, 92, 364, 1489, 6255, 26732, 116124, 510652, 2269052, 10173797, 45958102, 208995286, 955893438, 4394326977, 20293383562, 94096594300, 437913332281, 2044755438867, 9576471966384, 44974828618826, 211754505023066, 999332925620347, 4726331894418461, 22397883105780290, 106340208207251446

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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[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: A150395 A150396 A150397 * A150399 A150400 A150401

Adjacent sequences: A150395 A150396 A150397 * A150399 A150400 A150401

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved