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A148452 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, 0, 1), (0, 0, 1), (1, 1, -1)} 0
1, 1, 2, 6, 17, 51, 173, 575, 2019, 7243, 26322, 97884, 367911, 1400005, 5389926, 20912874, 81885031, 322824487, 1281038396, 5114281062, 20522900399, 82766997179, 335260408347, 1363570222423, 5566956645365, 22806255720589, 93734432354154, 386403758136640, 1597338230149405, 6620451269940699 (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, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 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: A181665 A186239 A148451 * A148453 A097514 A108630

Adjacent sequences:  A148449 A148450 A148451 * A148453 A148454 A148455

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified April 20 19:37 EDT 2014. Contains 240820 sequences.