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)).
Original entry on oeis.org
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
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.
A282169
a(n) is the minimal product of a positive integer sequence of length n with no duplicate substrings of length greater than 1, and every number different from its neighbors.
Original entry on oeis.org
1, 2, 2, 6, 6, 24, 24, 120, 120, 576, 720, 2880, 4320, 17280, 30240, 120960, 241920, 967680, 1935360, 8709120, 17418240, 87091200, 174182400, 870912000, 1741824000, 9580032000, 19160064000, 104509440000, 229920768000, 1149603840000, 2759049216000, 13795246080000, 33108590592000, 165542952960000, 430411677696000
Offset: 1
[1,1] is not a valid sequence because 1 is self-adjacent.
[1,2,3,1,2] is not valid because the substring [1,2] appears twice.
a(1) = 1 via [1];
a(2) = 2 via [1,2];
a(3) = 2 via [1,2,1];
a(4) = 6 via [1,2,1,3];
a(5) = 6 via [1,2,1,3,1];
a(6) = 24 via [1,2,1,3,1,4];
a(7) = 24 via [1,2,1,3,1,4,1];
a(8) = 120 via [1,2,1,3,1,4,1,5];
a(9) = 120 via [1,2,1,3,1,4,1,5,1];
a(10) = 576 via [1,2,1,3,1,4,2,3,4,1];
a(11) = 720 via [1,2,1,3,1,4,1,5,1,6,1].
A284431
The number of positive integer sequences of length n with no duplicate substrings of length greater than 1, every number different from its neighbors, and a minimal sum (= A282166(n)).
Original entry on oeis.org
1, 2, 1, 6, 2, 42, 12, 116, 18, 84, 168, 336, 384, 6864, 7872, 67392, 52800, 357120, 115200, 748800, 3093120, 11681280, 26853120, 43130880, 74649600, 2238382080, 3588157440, 51775856640, 63188398080, 653811056640, 480220876800, 4284050964480, 1316818944000, 11061279129600, 76921038028800
Offset: 1
For n = 5, the a(5) = 2 sequences are [1,3,1,2,1] and [1,2,1,3,1], each with a sum of A282166(5) = 8.
A284435
The number of positive integer sequences of length n with no duplicate substrings (forward or backward) of length greater than 1 and a minimal product (= A282193(n)).
Original entry on oeis.org
1, 1, 2, 2, 4, 4, 4, 48, 144, 144, 144, 2304, 2160, 8640, 8640, 8640, 161280, 806400, 806400, 806400, 38534400, 39168000, 108864000, 108864000, 2794176000, 5370624000, 10741248000, 21482496000, 286355865600, 1002245529600, 2004491059200, 4008982118400, 61212572467200, 244850289868800, 489700579737600
Offset: 1
For n = 7 the a(7) = 4 solutions are:
[1,3,3,2,2,1,1],
[1,2,2,3,3,1,1],
[1,1,3,3,2,2,1], and
[1,1,2,2,3,3,1].
A284436
The number of positive integer sequences of length n with no duplicate substrings (forward or backward) of length greater than 1, no self-adjacent terms, and a minimal product (= A282170(n)).
Original entry on oeis.org
1, 2, 6, 2, 18, 12, 24, 24, 792, 240, 1440, 720, 7488, 10080, 16992, 40320, 1013760, 725760, 979200, 3628800, 17902080, 79833600, 89510400, 479001600, 1988582400, 11446272000, 11931494400, 108138240000, 312309043200, 1539772416000, 2186163302400, 19872992563200
Offset: 1
For n = 4 the a(4) = 2 solutions are [1,3,2,1] and [1,2,3,1].
Name edited and terms a(9) onward added by
Max Alekseyev, Feb 06 2025
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