A150712 - OEIS

A150712

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

1, 2, 8, 27, 122, 499, 2214, 9842, 44530, 203920, 940733, 4372177, 20483297, 96217438, 454871743, 2156838988, 10261591892, 48987161073, 234370298197, 1124216923471, 5404012596212, 26022531847774, 125547200108280, 606608973049013, 2935239954436866, 14222485466148384, 68994436275698448

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..26.

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, -1 + k, -1 + n] + aux[i, -1 + j, -1 + 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

CROSSREFS

Sequence in context: A323613 A150710 A150711 * A150713 A383974 A276940

Adjacent sequences: A150709 A150710 A150711 * A150713 A150714 A150715

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved