A150925 - OEIS

A150925

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

1, 2, 9, 33, 149, 632, 2911, 13006, 60909, 279756, 1324645, 6189865, 29539507, 139630146, 670290631, 3194608107, 15405629210, 73879980430, 357568409984, 1723048366284, 8363909960364, 40458971651770, 196874510840924, 955330683139023, 4658278805030656, 22662963563493423, 110702220176118691

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

OFFSET

0,2

LINKS

Table of n, a(n) for n=0..26.

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[-1 + i, -1 + j, k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + j, 1 + 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: A150922 A150923 A150924 * A150926 A150927 A150928

Adjacent sequences: A150922 A150923 A150924 * A150926 A150927 A150928

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved