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A328299 Number of n-step walks on cubic lattice starting at (0,0,0), ending at (floor(n/3), floor((n+1)/3), floor((n+2)/3)), 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). 3
1, 1, 3, 12, 41, 179, 909, 3968, 19680, 106368, 516905, 2717631, 15139485, 77813569, 422589823, 2395441908, 12734635078, 70577595746, 404540380566, 2199035619696, 12356298623126, 71368686011040, 394076753535029, 2236273925952447, 12988459939106601 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1039

Wikipedia, Lattice path

Wikipedia, Self-avoiding walk

EXAMPLE

a(2) = 3: [(0,0,0),(1,0,0),(0,1,1)], [(0,0,0),(0,1,0),(0,1,1)], [(0,0,0),(0,0,1),(0,1,1)].

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-> b([floor((n+i)/3)$i=0..2]):

seq(a(n), n=0..24);

CROSSREFS

Cf. A006472, A022916, A328297, A328345.

Sequence in context: A017940 A038342 A260153 * A135264 A084529 A017941

Adjacent sequences:  A328296 A328297 A328298 * A328300 A328301 A328302

KEYWORD

nonn,walk

AUTHOR

Alois P. Heinz, Oct 11 2019

STATUS

approved

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Last modified January 29 16:58 EST 2020. Contains 331347 sequences. (Running on oeis4.)