A283558 The number of positive integer sequences of length n with no duplicate substrings of length greater than 1 and a minimal sum (= A259280(n)).

1, 1, 3, 2, 2, 6, 6, 48, 60, 168, 144, 288, 1872, 3744, 5760, 11520, 161280, 322560, 1866240, 2903040, 10782720, 8294400, 24883200, 282009600, 846028800, 3060633600, 9181900800, 10450944000, 31352832000, 668860416000, 1881169920000, 17850212352000, 41009504256000, 248816074752000, 381752082432000

Offset: 1

Author

Peter Kagey, Mar 10 2017

Keywords

• nonn

Examples

			For n = 7 the a(7) = 6 sequences are
1,3,1,2,2,1,1;
1,2,2,1,3,1,1;
1,3,1,1,2,2,1;
1,1,3,1,2,2,1;
1,2,2,1,1,3,1; and
1,1,2,2,1,3,1.
		

Crossrefs

A283557 is the product analog.

Cf. A259280, A284431, A284432, A284433.

Programs

Mathematica

s[1] = 1; s[n_] := Ceiling[(n+1+ Sum[Floor[Sqrt[2 k] + 1/2], {k, n-1}])/2]; subQ[w_] := Block[{n = Length@w}, Length@ Union@ Flatten[ Table[ Take[w, {i, j}], {j, 2, n}, {i, j - 1}], 1] == n (n-1)/2]; a[n_] := Sum[ Length@ Select[ Permutations@ e, subQ], {e, IntegerPartitions[ s[n], {n}]}]; Array[a, 10] (* Giovanni Resta, Mar 10 2017 *)

Extensions

a(11)-a(13) from Giovanni Resta, Mar 10 2017

Terms a(14) onward from Max Alekseyev, Feb 06 2025