A150336 - OEIS

A150336

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

1, 2, 7, 23, 84, 320, 1262, 5114, 21083, 88154, 372868, 1593621, 6871015, 29853188, 130548316, 574102027, 2537245436, 11263169847, 50200245088, 224556548825, 1007809545113, 4536610177289, 20477454773837, 92665005959394, 420308185091775, 1910551100747084, 8702049387822175, 39709772506902787

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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, j, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A151291 A150334 A150335 * A173519 A151292 A179533

Adjacent sequences: A150333 A150334 A150335 * A150337 A150338 A150339

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved