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A150855 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, 0, 1), (0, 1, 1), (1, -1, 1), (1, 0, -1), (1, 0, 1)} 0
1, 2, 8, 32, 141, 624, 2867, 13229, 62119, 292731, 1392647, 6644788, 31885950, 153374635, 740486213, 3582007538, 17372069719, 84385948890, 410681164286, 2001299076845, 9766585741966, 47714534077443, 233373742710965, 1142496798141894, 5598342122817010, 27453993432390512, 134736627872497064 (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, j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A150852 A150853 A150854 * A150856 A105483 A150857

Adjacent sequences:  A150852 A150853 A150854 * A150856 A150857 A150858

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified January 22 05:19 EST 2022. Contains 350481 sequences. (Running on oeis4.)