A148622 - OEIS

A148622

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

1, 1, 3, 6, 21, 59, 224, 778, 3074, 11996, 49040, 203505, 860069, 3696639, 16073620, 70742766, 314411761, 1409236688, 6367263724, 28958423806, 132525828708, 609812684776, 2819761081437, 13097700679165, 61082151474216, 285923856913975, 1342918625701453, 6326900756629652, 29893296939002381

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..28.

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, -1 + k, -1 + n] + aux[1 + i, 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: A148619 A148620 A148621 * A148623 A259273 A054878

Adjacent sequences: A148619 A148620 A148621 * A148623 A148624 A148625

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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