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A149139 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), (-1, 0, 0), (1, -1, 1), (1, 1, 0)} 0
1, 1, 4, 9, 36, 110, 440, 1485, 6038, 21770, 90166, 335868, 1405402, 5375252, 22720338, 88585501, 376880976, 1490018552, 6375130214, 25514622182, 109661163910, 442953363234, 1910605636686, 7780053826624, 33664098882158, 138014571325972, 598708608700234, 2468677410383886, 10733193310292636 (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, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, 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: A018224 A149137 A149138 * A149140 A239230 A149141

Adjacent sequences:  A149136 A149137 A149138 * A149140 A149141 A149142

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified May 25 21:44 EDT 2022. Contains 354071 sequences. (Running on oeis4.)