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A150043 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), (0, 0, 1), (0, 1, 1), (1, 1, -1)} 0
1, 2, 6, 18, 60, 204, 716, 2560, 9296, 34128, 126560, 472864, 1778016, 6722880, 25536768, 97384128, 372691968, 1430618112, 5506231808, 21244025088, 82137286400, 318177976064, 1234689470976, 4798686523904, 18676787597824, 72786442978304, 283997288733696, 1109305183011840, 4337384738945024 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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[i, -1 + j, -1 + k, -1 + n] + aux[i, 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: A005566 A005631 A118677 * A048117 A048118 A004113

Adjacent sequences:  A150040 A150041 A150042 * A150044 A150045 A150046

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified November 14 15:13 EST 2019. Contains 329126 sequences. (Running on oeis4.)