A149350 - OEIS

A149350

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

1, 1, 4, 12, 42, 156, 593, 2281, 9007, 35980, 144820, 588319, 2409154, 9915930, 41011199, 170436891, 711045649, 2975942110, 12494155666, 52604269433, 222018315817, 939132096649, 3980901402084, 16906905614935, 71928191115056, 306508303374156, 1308116731888692, 5590618748977314

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OFFSET

0,3

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, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A173411 A149348 A149349 * A149351 A149352 A149353

Adjacent sequences: A149347 A149348 A149349 * A149351 A149352 A149353

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved