A150191 - OEIS

A150191

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

1, 2, 6, 21, 78, 304, 1231, 5125, 21763, 93925, 410918, 1817984, 8119903, 36558593, 165753451, 756139942, 3468044808, 15982873453, 73974648811, 343704693702, 1602527924763, 7495558935633, 35161017268936, 165375339796179, 779722811553856, 3684589801749848, 17447964172451089, 82783211278892060

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

OFFSET

0,2

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, j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, 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: A216490 A150190 A356780 * A150192 A287211 A357538

Adjacent sequences: A150188 A150189 A150190 * A150192 A150193 A150194

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved