A150652 - OEIS

A150652

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

1, 2, 7, 28, 119, 520, 2346, 10755, 49917, 234022, 1105325, 5252101, 25078973, 120239390, 578443647, 2790846344, 13498704672, 65431808670, 317767458122, 1545814600692, 7530993648957, 36738898821929, 179440759231967, 877379773325019, 4294205895482281, 21036313171931658, 103137207715018154

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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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A150651 A151298 A161944 * A130655 A150653 A150654

Adjacent sequences: A150649 A150650 A150651 * A150653 A150654 A150655

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved