A283558 The number of positive integer sequences of length n with no duplicate substrings and a minimal sum (i.e., the sum of the sequence is A259280(n)).

1, 1, 3, 2, 2, 6, 6, 48, 60, 168, 144, 288, 1872

Offset

1,3

Links

Table of n, a(n) for n=1..13.

Example

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.

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 *)

Crossrefs

Cf. A259280. A283557 is the product analog.

Sequence in context: A197586 A111702 A283557 * A234713 A091029 A272372

Adjacent sequences: A283555 A283556 A283557 * A283559 A283560 A283561

Keyword

nonn,more

Author

Peter Kagey, Mar 10 2017

Extensions

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

Status

approved