A151033 - OEIS

A151033

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

1, 3, 9, 31, 111, 397, 1465, 5479, 20495, 77641, 296045, 1129451, 4337187, 16717677, 64478697, 249647575, 968902903, 3762652881, 14648257893, 57120858211, 222864458027, 871020059445, 3408282334305, 13343034152015, 52300840360703, 205189696478169, 805359505872541, 3163918570564827

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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, -1 + j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, j, -1 + 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: A128082 A148970 A151459 * A047012 A120305 A049170

Adjacent sequences: A151030 A151031 A151032 * A151034 A151035 A151036

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved