The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A328270 Total number of nodes in all walks on cubic lattice starting at (0,0,0), ending at (0,n,n), 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). 1
 1, 9, 130, 2401, 50346, 1141030, 27222364, 673340265, 17104148290, 443406172278, 11680186909062, 311667574680190, 8404755004516300, 228659546010880620, 6267500870514732780, 172891678107177498193, 4795723803862121368590, 133668769806498536349670 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..17. Wikipedia, Lattice path Wikipedia, Self-avoiding walk FORMULA a(n) = (2n+1) * A328269(n). a(n) is odd <=> n in { A000225 }. EXAMPLE a(1) = 9: nodes in [(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-> (2*n+1)*b([0, n\$2]): 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_] := (2n+1) b[{0, n, n}]; a /@ Range[0, 23] (* Jean-François Alcover, May 13 2020, after Maple *) CROSSREFS Cf. A000225, A328269. Sequence in context: A287690 A075762 A349155 * A060944 A299596 A200407 Adjacent sequences: A328267 A328268 A328269 * A328271 A328272 A328273 KEYWORD nonn,walk AUTHOR Alois P. Heinz, Oct 10 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified February 26 04:47 EST 2024. Contains 370335 sequences. (Running on oeis4.)