A148693 - OEIS

A148693

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

1, 1, 3, 7, 23, 67, 237, 805, 2885, 10445, 39679, 148885, 573215, 2242027, 8857871, 35069977, 141098599, 572026433, 2327192345, 9529746879, 39375349267, 163259808875, 679323714809, 2843675504507, 11960396769469, 50428215090523, 213406038719425, 907014855445347, 3865740278475333

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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, j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A201204 A106964 A096019 * A148694 A148695 A148696

Adjacent sequences: A148690 A148691 A148692 * A148694 A148695 A148696

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved