A148444 - OEIS

A148444

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

1, 1, 2, 6, 16, 47, 157, 517, 1754, 6284, 22342, 82117, 305289, 1145162, 4369073, 16760959, 64992835, 253932749, 998432537, 3953538052, 15737751848, 62980503415, 253282002983, 1022864094559, 4148173714710, 16884795747618, 68964936191558, 282616900004462, 1161546491366627, 4787684370830771

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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, -1 + j, k, -1 + 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, -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: A190729 A071726 A148443 * A064190 A151281 A045694

Adjacent sequences: A148441 A148442 A148443 * A148445 A148446 A148447

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved