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A149375 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), (-1, 0, 1), (0, 1, -1), (1, 0, -1), (1, 0, 1)} 0
1, 1, 4, 12, 47, 164, 695, 2699, 11928, 48830, 220914, 940961, 4321991, 18937219, 87972118, 393301987, 1843766751, 8369121619, 39519636049, 181547249045, 862251480517, 3999666690154, 19086139896338, 89240905816222, 427543488272411, 2012304113539057, 9673425072162760, 45783191013294482 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + 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: A101225 A000775 A149374 * A035310 A022016 A151441

Adjacent sequences:  A149372 A149373 A149374 * A149376 A149377 A149378

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified November 15 08:37 EST 2019. Contains 329144 sequences. (Running on oeis4.)