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 A346541 Number of walks on square lattice from (n,2n) to (0,0) using steps that decrease the Euclidean distance to the origin and increase the Euclidean distance to (n,2n) and that change each coordinate by at most 1. 2
 1, 5, 173, 6273, 327304, 19662204, 1331125733, 97103842536, 7486548949630, 600824064355643, 49716537270181030, 4212436222856773156, 363673201239600512658, 31874623637580787947172, 2828388650238276648013964, 253555200931317108300020394, 22925898959060646660438636660 (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..200 Alois P. Heinz, Animation of a(2) = 173 walks Wikipedia, Counting lattice paths Wikipedia, Self-avoiding walk FORMULA a(n) = A346540(2n,n) = A346540(n,2n). 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, 2*n]\$2): seq(a(n), n=0..20); 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, 2n}, {n, 2n}]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Nov 04 2021, after Alois P. Heinz *) CROSSREFS Cf. A346540. Sequence in context: A139986 A354573 A123111 * A303154 A060070 A300590 Adjacent sequences: A346538 A346539 A346540 * A346542 A346543 A346544 KEYWORD nonn,walk AUTHOR Alois P. Heinz, Sep 16 2021 STATUS approved

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Last modified December 6 12:26 EST 2023. Contains 367601 sequences. (Running on oeis4.)