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A148433 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, 1), (0, 1, -1), (0, 1, 0), (1, -1, 1)} 0
1, 1, 2, 5, 19, 62, 239, 864, 3566, 13868, 58920, 239080, 1036763, 4332325, 19075298, 81448735, 362573593, 1573070743, 7063456476, 31032442606, 140305062067, 622585027321, 2830717307941, 12663320633915, 57847182842753, 260530394622910, 1194859922437770, 5411945823430944, 24905346976487567 (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, -1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + 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: A320276 A148432 A047116 * A148434 A341762 A341878

Adjacent sequences:  A148430 A148431 A148432 * A148434 A148435 A148436

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified June 21 15:17 EDT 2021. Contains 345364 sequences. (Running on oeis4.)