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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A347947 Number of walks on square lattice from (1,n) to (0,0) using steps that decrease the Euclidean distance to the origin and increase the Euclidean distance to (n,1) and that change each coordinate by at most 1. 2
 1, 3, 5, 24, 81, 298, 1070, 3868, 13960, 50417, 182084, 657707, 2375894, 8583264, 31009890, 112038032, 404803299, 1462624643, 5284813128, 19095564020, 68998567080, 249316670981, 900876831495, 3255230444720, 11762504284218, 42502963168784, 153581776819904 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Lattice points may have negative coordinates, and different walks may differ in length. All walks are self-avoiding. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 Alois P. Heinz, Animation of a(5) = 298 walks Wikipedia, Counting lattice paths Wikipedia, Self-avoiding walk MAPLE s:= proc(n) option remember; `if`(n=0, [[]], map(x-> seq([x[], i], i=-1..1), s(n-1))) end: b:= proc(l, v) option remember; (n-> `if`(l=[0\$n], 1, add((h-> `if`( add(i^2, i=h)add(i^2, i=v-l) , b(h, v), 0))(l+x), x=s(n))))(nops(l)) end: a:= n-> b([n, 1]\$2): seq(a(n), n=0..30); MATHEMATICA s[n_] := s[n] = If[n == 0, {{}}, Sequence @@ Table[Append[#, i], {i, -1, 1}]& /@ s[n-1]]; b[l_, v_] := b[l, v] = With[{n = Length[l]}, If[l == Table[0, {n}], 1, Sum[With[{h = l + x}, If[h.h(v-l).(v-l), b[h, v], 0]], {x, s[n]}]]]; a[n_] := b[{n, 1}, {n, 1}]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Nov 04 2021, after Alois P. Heinz *) CROSSREFS Column (or row) k=1 of A346540. Sequence in context: A230985 A286427 A290509 * A208800 A356274 A249935 Adjacent sequences: A347944 A347945 A347946 * A347948 A347949 A347950 KEYWORD nonn,walk AUTHOR Alois P. Heinz, Sep 20 2021 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 April 15 02:01 EDT 2024. Contains 371667 sequences. (Running on oeis4.)