A150714 - OEIS

A150714

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

1, 2, 8, 28, 104, 400, 1536, 5936, 23264, 91072, 357632, 1412480, 5577984, 22061568, 87511040, 347153152, 1378358784, 5481688064, 21803069440, 86767978496, 345644969984, 1377055006720, 5488195010560, 21886712078336, 87292178644992, 348239502868480, 1389828709679104, 5547292146991104

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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, -1 + k, -1 + n] + aux[-1 + i, -1 + j, k, -1 + n] + aux[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: A133592 A115967 A357641 * A292668 A122447 A150715

Adjacent sequences: A150711 A150712 A150713 * A150715 A150716 A150717

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved