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A148446 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, -1, 1), (-1, 1, 1), (0, 1, 1), (1, 0, -1)} 0
1, 1, 2, 6, 17, 49, 170, 567, 1938, 7048, 25692, 94221, 355939, 1358403, 5196687, 20169943, 79178940, 311341768, 1233884011, 4934811327, 19786170788, 79683695476, 323069731308, 1313959977470, 5358853327284, 21960167792626, 90282256030304, 371942734756058, 1537483777024417, 6374355298767209 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..29.

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, 1 + 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: A122099 A026165 A148445 * A244401 A244402 A244403

Adjacent sequences:  A148443 A148444 A148445 * A148447 A148448 A148449

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified February 20 12:38 EST 2019. Contains 320327 sequences. (Running on oeis4.)