A151248 - OEIS

A151248

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

1, 4, 17, 77, 359, 1702, 8165, 39490, 192131, 939016, 4605451, 22650627, 111651643, 551379076, 2727090199, 13505347559, 66955102057, 332249446722, 1650027506813, 8200076776267, 40776104773443, 202872003528704, 1009809751924771, 5028455914303228, 25048822763861523, 124818886054490310

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..25.

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, -1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 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: A333059 A081922 A124325 * A104455 A123952 A005494

Adjacent sequences: A151245 A151246 A151247 * A151249 A151250 A151251

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved