A148716 - OEIS

A148716

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

1, 1, 3, 7, 24, 70, 264, 871, 3445, 12209, 49965, 186006, 778897, 3005994, 12798041, 50759402, 218926582, 887015121, 3865566214, 15933181036, 70025009803, 292737848952, 1295655376440, 5480826330146, 24403529986073, 104271056911262, 466660480654007, 2011199904443749, 9041319778456309

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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, -1 + j, 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, 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: A148713 A148714 A148715 * A148717 A148718 A003449

Adjacent sequences: A148713 A148714 A148715 * A148717 A148718 A148719

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved