A150026 - OEIS

A150026

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

1, 2, 5, 19, 74, 272, 1128, 4785, 19680, 85534, 375994, 1621412, 7228110, 32438712, 143597689, 649971056, 2955472000, 13301538596, 60825607272, 279067019064, 1270235883915, 5851260862078, 27020828578132, 123996284280459, 574325273769182, 2665349207045963, 12306252890649850, 57243664510934520

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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, j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, -1 + j, 1 + 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: A106873 A014273 A255541 * A150027 A277969 A058131

Adjacent sequences: A150023 A150024 A150025 * A150027 A150028 A150029

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved