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A328427 Number of 2n-step walks on cubic lattice starting at (0,0,0), ending at (n,y,z), remaining in the first (nonnegative) octant and using steps (0,0,1), (0,1,0), (1,0,0), (-1,1,1), (1,-1,1), and (1,1,-1). 2
1, 6, 93, 2040, 52086, 1443898, 42073956, 1266666928, 39005460010, 1220921798726, 38687295919777, 1237507863154364, 39880747868561408, 1292960017095690800, 42125333404129589074, 1378096053159532505284, 45239194620411006084462, 1489461895371375668384236 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..500

FORMULA

a(n) = A328297(2n,n).

MAPLE

b:= proc(l) option remember; `if`(l[-1]=0, 1, (r-> add(

      add(add(`if`(i+j+k=1, (h-> `if`(h[1]<0, 0, b(h)))(

      sort(l-[i, j, k])), 0), k=r), j=r), i=r))([$-1..1]))

    end:

a:= n-> add(b(sort([n, j, n-j])), j=0..n):

seq(a(n), n=0..23);

MATHEMATICA

b[l_] := b[l] = If[Last[l] == 0, 1, Function[r, Sum[If[i + j + k == 1, Function[h, If[h[[1]] < 0, 0, b[h]]][Sort[l - {i, j, k}]], 0], {i, r}, {j, r}, {k, r}]][{-1, 0, 1}]];

a[n_] := Sum[b[Sort[{n, j, n - j}]], {j, 0, n}];

a /@ Range[0, 23] (* Jean-Fran├žois Alcover, May 13 2020, after Maple *)

CROSSREFS

Cf. A328297.

Sequence in context: A053512 A331623 A158121 * A103212 A033935 A218682

Adjacent sequences:  A328424 A328425 A328426 * A328428 A328429 A328430

KEYWORD

nonn,walk

AUTHOR

Alois P. Heinz, Oct 15 2019

STATUS

approved

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Last modified May 17 12:55 EDT 2021. Contains 343971 sequences. (Running on oeis4.)