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A149188 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, 0, 1), (-1, 1, -1), (0, 1, -1), (1, 0, 1)} 0
1, 1, 4, 10, 37, 126, 470, 1757, 6821, 26562, 105818, 423428, 1716182, 6992321, 28716249, 118480304, 491549494, 2047242541, 8561397677, 35918756167, 151171279767, 637943008302, 2698970504329, 11444255979602, 48628209832546, 207019652700133, 882879856348389, 3771329321179581 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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, 1 + 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

CROSSREFS

Sequence in context: A079725 A154152 A025237 * A149189 A149190 A102755

Adjacent sequences:  A149185 A149186 A149187 * A149189 A149190 A149191

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified February 19 16:02 EST 2019. Contains 320311 sequences. (Running on oeis4.)