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 A149424 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), (0, 0, -1), (1, 1, 1)}. 3
 1, 1, 4, 13, 40, 136, 496, 1753, 6256, 22912, 85216, 314836, 1170688, 4396048, 16623328, 62744017, 237680992, 904962400, 3459831424, 13219219972, 50621972224, 194465172304, 749061374848, 2884682636764, 11126422372864, 43007603099296, 166555051934848, 644984620465264, 2500560314630656 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..300 A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899. FORMULA a(n) == 1 (mod 3). - Alois P. Heinz, Jul 12 2021 MAPLE b:= proc(n, l) option remember; `if`(n=0, 1, b(n-1, map(x-> x+1, l))+       add(`if`(l[i]>0, b(n-1, sort(subsop(i=l[i]-1, l))), 0), i=1..3))     end: a:= n-> b(n, [0\$3]): seq(a(n), n=0..30);  # Alois P. Heinz, Jan 26 2021 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, j, 1 + 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 Cf. A151265. Column k=3 of A335570. Sequence in context: A227747 A094628 A034742 * A097112 A222270 A213496 Adjacent sequences:  A149421 A149422 A149423 * A149425 A149426 A149427 KEYWORD nonn,walk AUTHOR Manuel Kauers, Nov 18 2008 STATUS approved

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Last modified December 7 17:17 EST 2021. Contains 349582 sequences. (Running on oeis4.)