A283557 The number of positive integer sequences of length n with no duplicate substrings of length greater than 1 and a minimal product (= A282164(n)).

1, 1, 3, 2, 2, 6, 6, 24, 24, 120, 120, 1200, 1440, 4320, 4320, 8640, 30240, 60480, 483840, 967680, 1935360, 3870720, 17418240, 34836480, 348364800, 696729600, 1741824000, 3483648000, 19160064000, 38320128000, 689762304000, 1379524608000, 9656672256000, 16554295296000, 66217181184000

Offset

1,3

Comments

Surprisingly, a(n) = A282164(n) for n in { 1, 2, 4, 6, 8, 10, 13, 14, 19, 25, 32, 34, 35, ... }. - Max Alekseyev, Feb 06 2025

Links

Table of n, a(n) for n=1..35.

Peter Kagey, Examples of all sequences a(1)-a(10).

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.

Crossrefs

A283558 is the sum analog.

Cf. A282164, A284434, A284435, A284436.

Sequence in context: A272332 A197586 A111702 * A283558 A234713 A091029

Adjacent sequences: A283554 A283555 A283556 * A283558 A283559 A283560

Keyword

nonn

Author

Peter Kagey, Mar 10 2017

Extensions

Terms a(11) onward from Max Alekseyev, Feb 06 2025

Status

approved