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A148488 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, 1), (-1, 1, 0), (0, -1, 1), (0, 0, 1), (1, 1, -1)} 0
1, 1, 2, 6, 21, 73, 272, 1054, 4214, 17226, 71623, 302252, 1292432, 5581926, 24319777, 106774166, 471860548, 2097325988, 9369510453, 42044499840, 189429350786, 856534717875, 3885495872594, 17677575370337, 80641091022357, 368762780681781, 1690078200540330, 7761698620206097, 35713157961834317 (list; graph; refs; listen; history; text; internal format)
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[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, 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: A116781 A047106 A148487 * A148489 A116771 A294765

Adjacent sequences:  A148485 A148486 A148487 * A148489 A148490 A148491

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified June 25 22:13 EDT 2022. Contains 354868 sequences. (Running on oeis4.)