A148073 - OEIS

A148073

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

1, 1, 2, 4, 9, 21, 56, 153, 431, 1269, 3748, 11283, 34892, 109201, 346671, 1113914, 3599997, 11754161, 38738445, 128543670, 429827021, 1444670782, 4879545858, 16575721093, 56568953256, 193962159926, 667744908521, 2306563486959, 7996271742308, 27813368946061, 97050437964778, 339653854810804, 1191781442742137

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..32.

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[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: A005217 A148072 A001430 * A057513 A006080 A287694

Adjacent sequences: A148070 A148071 A148072 * A148074 A148075 A148076

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved