A148476 - OEIS

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A148476

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

1, 1, 2, 6, 20, 67, 238, 889, 3430, 13502, 54133, 220602, 912169, 3814549, 16105873, 68586793, 294388261, 1272134186, 5530081563, 24168691099, 106150861556, 468293726986, 2074232732996, 9221208846420, 41133693548902, 184061536758043, 825997748283384, 3716645799512423, 16765083601178960

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Table of n, a(n) for n=0..28.

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[i, 1 + j, k, -1 + n] + aux[1 + i, -1 + j, -1 + 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: A285197 A372872 A148475 * A148477 A369123 A027063

Adjacent sequences: A148473 A148474 A148475 * A148477 A148478 A148479

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved