A150299 - OEIS

A150299

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

1, 2, 6, 24, 98, 412, 1840, 8154, 37224, 171160, 793154, 3716730, 17465560, 82664746, 392713914, 1872141724, 8959486334, 42973967858, 206712819136, 996416355570, 4812329849512, 23285606526834, 112842422049906, 547665328751596, 2661489800389408, 12949604740884364, 63078260567268032, 307567027977622324

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..27.

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, -1 + 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, 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: A053504 A215716 A060725 * A094012 A141253 A306672

Adjacent sequences: A150296 A150297 A150298 * A150300 A150301 A150302

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved