A331623 Number of sequences with n copies each of 1,2,...,n avoiding absolute differences between adjacent elements larger than one.

1, 1, 6, 92, 11482, 8956752, 54331653686, 2535604038015218, 951645881858020642746, 2911820015993491302722966990, 73784388170659542104264761249115686, 15642058800086197220958447712819197014917632, 27980772370697320617389378491983217784996780441605354

Offset: 0

Author

Alois P. Heinz, Jan 22 2020

Keywords

• nonn

Examples

			a(0) = 1: the empty sequence.
a(1) = 1: 1.
a(2) = 6: 1122, 1212, 1221, 2112, 2121, 2211.
a(3) = 92: 111222333, 111223233, 111223323, 111223332, ..., 333221112, 333221121, 333221211, 333222111.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..25

Crossrefs

Main diagonal of A331562.

Cf. A034841.

Programs

Maple

b:= proc(l, q) option remember; (n-> `if`(n<2, 1, add(
     `if`(l[j]=1, `if`(j in [1, n], b(subsop(j=[][], l),
     `if`(j=1, 0, n)), 0), b(subsop(j=l[j]-1, l), j)), j=
     `if`(q<0, 1..n, max(1, q-1)..min(n, q+1)))))(nops(l))
    end:
a:= n-> b([n$n], -1):
seq(a(n), n=0..6);

Mathematica

b[l_, q_] := b[l, q] = With[{n = Length[l]}, If[n < 2, 1, Sum[
      If[l[[j]] == 1, If[j == 1 || j == n, b[ReplacePart[l, j -> Nothing],
      If[j == 1, 0, n]], 0], b[ReplacePart[l, j -> l[[j]] - 1], j]], {j,
      If[q < 0, Range[n], Range[Max[1, q - 1], Min[n, q + 1]]]}]]];
a[n_] := b[Table[n, {n}], -1];
Table[Print[n, " ", a[n]]; a[n], {n, 0, 8}] (* Jean-François Alcover, Jan 04 2021, after Alois P. Heinz *)

Formula

a(n) = A331562(n,n).

Extensions

a(9)-a(12) (using new data provided by Andrew Howroyd in A331562) from Alois P. Heinz, Sep 01 2020