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A277262 Number of walks on cubic lattice starting at (1,1,1), ending at (n,n,n), remaining in the first (nonnegative) octant and using steps (0,-1,2), (0,2,-1), (-1,0,2), (2,0,-1), (-1,2,0), and (2,-1,0). 3
0, 1, 12, 456, 54216, 6932916, 1069256400, 170663949024, 29130191148240, 5115288488816760, 927446504770571520, 171486284915686699620, 32295496327107026335392, 6164943698859825359296740, 1190940852937573264531168944, 232287567721717805821704554232 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..400

FORMULA

a(n) ~ c * 6^(3*n) / n, where c = 0.000020280187096503586851533... . - Vaclav Kotesovec, Oct 14 2016

MAPLE

g():= combinat[permute]([0, -1, 2]):

b:= proc(l) option remember; `if`(l=[1$3], 1, add((p->

      `if`(p[1]<0, 0, b(p)))(sort(l-x)), x=g()))

    end:

a:= n-> b([n$3]):

seq(a(n), n=0..20);

MATHEMATICA

g = Permutations[{0, -1, 2}];

b[l_] := b[l] = If[l == {1, 1, 1}, 1, Sum[Function[p, If[p[[1]] < 0, 0, b[p]]][Sort[l - x]], {x, g}]];

a[n_] := b[{n, n, n}];

Table[a[n], {n, 0, 20}] (* Jean-Fran├žois Alcover, Mar 29 2017, translated from Maple *)

CROSSREFS

Cf. A048116.

Sequence in context: A202799 A121348 A239365 * A226358 A225796 A112363

Adjacent sequences:  A277259 A277260 A277261 * A277263 A277264 A277265

KEYWORD

nonn,walk

AUTHOR

Alois P. Heinz, Oct 07 2016

STATUS

approved

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Last modified October 21 11:25 EDT 2019. Contains 328295 sequences. (Running on oeis4.)