

A150420


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), (1, 0, 0), (1, 0, 1), (1, 1, 1)}


0



1, 2, 7, 24, 95, 381, 1618, 6947, 30662, 136573, 618099, 2818128, 12981409, 60152326, 280713698, 1316221777, 6203507127, 29349414927, 139399848256, 664156567450, 3174024450836, 15207455409058, 73041930090888, 351566863640124, 1695586707912644, 8192282542679420, 39647874861987388, 192172115316412119
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OFFSET

0,2


LINKS

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, j, 1 + k, 1 + n] + aux[1 + i, 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



KEYWORD

nonn,walk


AUTHOR



STATUS

approved



