

A149427


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


0



1, 1, 4, 13, 44, 150, 548, 1979, 7324, 27074, 101620, 381338, 1444860, 5478476, 20902380, 79824913, 306175148, 1175699494, 4528970884, 17465198198, 67512268620, 261240684772, 1012744843508, 3929870352586, 15272109227396, 59401882159868, 231326540050700, 901564182638872, 3517261162906916
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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, 1 + j, 1 + k, 1 + n] + aux[1 + i, j, 1 + k, 1 + n] + aux[1 + i, 1 + j, 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: A027127 A326329 A073717 * A290907 A252933 A229397
Adjacent sequences: A149424 A149425 A149426 * A149428 A149429 A149430


KEYWORD

nonn,walk


AUTHOR

Manuel Kauers, Nov 18 2008


STATUS

approved



