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A148694 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, 1, -1), (0, 1, 1), (1, 0, -1)} 0
1, 1, 3, 7, 23, 67, 237, 805, 2885, 10509, 39807, 149141, 579341, 2263291, 8905423, 35534405, 143264965, 578222653, 2363626881, 9716589785, 40034773345, 166371602771, 694827197783, 2906176160045, 12238781990415, 51736232838013, 219012786708273, 932089077079915, 3979322489517421 (list; graph; refs; listen; history; text; internal format)
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, -1 + 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: A106964 A096019 A148693 * A148695 A148696 A148697

Adjacent sequences:  A148691 A148692 A148693 * A148695 A148696 A148697

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified December 3 14:45 EST 2016. Contains 278745 sequences.