A149346 - OEIS

A149346

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, 0), (1, -1, 0), (1, -1, 1), (1, 0, -1), (1, 1, 0)}.

1, 1, 4, 12, 42, 149, 568, 2172, 8578, 34181, 139057, 569719, 2364946, 9881270, 41674337, 176735488, 754733091, 3238354312, 13970248201, 60513360263, 263262526696, 1149346431161, 5035888179481, 22132171128821, 97564507265020, 431236737233659, 1911053967488337, 8488822597541547

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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, -1 + j, 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] + aux[1 + i, 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: A135489 A100217 A149345 * A149347 A173411 A149348

Adjacent sequences: A149343 A149344 A149345 * A149347 A149348 A149349

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved