A150264 - OEIS

A150264

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

1, 2, 6, 22, 88, 372, 1632, 7350, 33744, 157188, 740522, 3519904, 16851570, 81150912, 392687942, 1907901166, 9301268766, 45476190968, 222895010996, 1094818072024, 5387474604008, 26553803662396, 131062764352214, 647692832232724, 3204298760223824, 15867809689100878, 78645597680434374

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..26.

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, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, j, -1 + 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: A365246 A333080 A096267 * A294593 A214358 A107944

Adjacent sequences: A150261 A150262 A150263 * A150265 A150266 A150267

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved