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A150279 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), (0, 1, 1), (1, 0, -1), (1, 0, 0)} 0
1, 2, 6, 23, 89, 366, 1561, 6769, 30039, 134844, 612578, 2810228, 12981757, 60400299, 282517353, 1327885926, 6268368794, 29695994753, 141157315621, 672914374614, 3216240157019, 15408786613744, 73977869582241, 355861253079682, 1714836748695087, 8276836894125192, 40008433290430771, 193655372835566275 (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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[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: A190910 A150277 A150278 * A150280 A303071 A150281

Adjacent sequences:  A150276 A150277 A150278 * A150280 A150281 A150282

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified October 20 05:51 EDT 2020. Contains 337897 sequences. (Running on oeis4.)