A148945 - OEIS

A148945

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

1, 1, 3, 9, 29, 104, 390, 1482, 5872, 23670, 96862, 402409, 1691824, 7184785, 30771333, 132773241, 577026236, 2521811081, 11077691844, 48908119250, 216832245702, 964920349669, 4309740197244, 19311403519650, 86782764283827, 391070601747452, 1766791977497850, 8000592935633367, 36308193503404528

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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, j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A293070 A060719 A091152 * A177255 A136628 A151031

Adjacent sequences: A148942 A148943 A148944 * A148946 A148947 A148948

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved