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A150783 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, 0, 0), (1, 0, -1), (1, 0, 0), (1, 1, 1)} 0
1, 2, 8, 30, 134, 569, 2628, 11761, 55410, 255462, 1218653, 5721052, 27511880, 130716602, 632222509, 3029641905, 14716411060, 70967847363, 345870276570, 1675939150819, 8189428125892, 39831988941807, 195055025046631, 951574334402940, 4668069413448681, 22829043542171082, 112157691662007826 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..26.

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, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, 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: A150780 A150781 A150782 * A150784 A150785 A036723

Adjacent sequences:  A150780 A150781 A150782 * A150784 A150785 A150786

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified September 28 19:56 EDT 2021. Contains 347717 sequences. (Running on oeis4.)