A148266 - OEIS

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A148266

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

1, 1, 2, 4, 14, 33, 121, 341, 1364, 4118, 17156, 55195, 235565, 792216, 3452019, 12003317, 53078631, 189709685, 848602623, 3101364840, 14005457308, 52145063041, 237321022029, 897692005813, 4112322051292, 15768430719310, 72639898419924, 281851285839992, 1304668602752431, 5115278912246703

(list; graph; refs; listen; history; text; internal format)

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, k, -1 + n] + aux[-1 + 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] + 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: A148263 A148264 A148265 * A000622 A088028 A327459

Adjacent sequences: A148263 A148264 A148265 * A148267 A148268 A148269

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved