A148037 - OEIS

A148037

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

1, 1, 2, 3, 8, 17, 55, 137, 489, 1337, 4963, 14489, 56081, 172374, 685860, 2193107, 8924006, 29455832, 121957898, 413105672, 1734505507, 6003091829, 25496609376, 89865317945, 385361938143, 1379626758090, 5964466413469, 21644518493658, 94229149045835, 346030467616141, 1515554809560380, 5624080488702325

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..31.

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, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A148034 A148035 A148036 * A345324 A290383 A099960

Adjacent sequences: A148034 A148035 A148036 * A148038 A148039 A148040

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved