A150246 - OEIS

A150246

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

1, 2, 6, 22, 84, 349, 1489, 6522, 29167, 131937, 604928, 2795191, 13026035, 61071104, 287955729, 1364135422, 6488835986, 30978176466, 148354824082, 712491943840, 3430294543918, 16552408346485, 80031153498705, 387658022884679, 1880841554614987, 9139197220529013, 44469134400275800, 216648203834175807

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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, 1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, 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: A150244 A151288 A150245 * A055700 A279563 A150247

Adjacent sequences: A150243 A150244 A150245 * A150247 A150248 A150249

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved