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A148487 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), (0, -1, 1), (0, 0, 1), (1, -1, 1), (1, 1, -1)} 0
1, 1, 2, 6, 21, 73, 267, 1022, 4041, 16303, 66951, 279275, 1180486, 5043381, 21742492, 94484328, 413498117, 1820760068, 8060811170, 35859891401, 160225912174, 718718698186, 3235377214256, 14611428489991, 66182167582839, 300581687682479, 1368556033741457, 6245359601314856, 28560955419335974 (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[-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, 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: A116837 A116781 A047106 * A148488 A148489 A116771

Adjacent sequences:  A148484 A148485 A148486 * A148488 A148489 A148490

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified June 26 16:31 EDT 2022. Contains 354885 sequences. (Running on oeis4.)