A148074 - OEIS

A148074

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

1, 1, 2, 4, 9, 21, 56, 164, 472, 1443, 4442, 13543, 42538, 140125, 461051, 1540007, 5230724, 17608645, 59481321, 206130290, 720298004, 2523815677, 8951596054, 31724219609, 111972880599, 399889272475, 1443126871712, 5216771470535, 18978785870361, 69268966498148, 251874465187235, 919122479206908, 3382867597156114

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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, 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: A057513 A006080 A287694 * A130866 A123458 A048194

Adjacent sequences: A148071 A148072 A148073 * A148075 A148076 A148077

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved