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A150014 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), (0, 1, -1), (0, 1, 0), (1, 0, 1)} 0
1, 2, 5, 18, 66, 234, 931, 3768, 14868, 62079, 262221, 1088156, 4673851, 20235559, 86466939, 378333205, 1664920163, 7252032306, 32147861808, 143128870572, 631965293765, 2828788664820, 12705192301169, 56670108122926, 255577539573779, 1155787880338026, 5196053668562184, 23574579310744286 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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, k, -1 + n] + aux[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: A093635 A024025 A084518 * A150015 A150016 A150017

Adjacent sequences:  A150011 A150012 A150013 * A150015 A150016 A150017

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified October 17 11:47 EDT 2019. Contains 328108 sequences. (Running on oeis4.)