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.
A284434
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 product (= A282169(n)).
Original entry on oeis.org
1, 2, 1, 6, 2, 24, 6, 120, 24, 84, 192, 336, 360, 1680, 2160, 10080, 26640, 70560, 80640, 564480, 645120, 13789440, 10644480, 78382080, 43545600, 783820800, 435456000, 2264371200, 12454041600, 22643712000, 117747302400, 466460467200, 367873228800, 2391175987200, 4414478745600
Offset: 1
For n = 7 the a(7) = 6 solutions are:
[1,4,1,3,1,2,1],
[1,3,1,4,1,2,1],
[1,4,1,2,1,3,1],
[1,2,1,4,1,3,1],
[1,3,1,2,1,4,1], and
[1,2,1,3,1,4,1].
A284432
The number of positive integer sequences of length n with no duplicate substrings (forward or backward) of length greater than 1 and a minimal sum (= A282168(n)).
Original entry on oeis.org
1, 1, 2, 2, 4, 4, 4, 48, 48, 144, 144, 144, 2160, 8496, 21312, 110592, 203904, 407808, 815616, 1631232, 15667200, 31334400, 445114368, 890228736, 7291772928, 14583545856, 36458864640, 72917729280, 145835458560, 1694545920000, 16054441574400, 101226251059200, 421941436416000, 2144473989120000, 13603849760931840
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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