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)).
Original entry on oeis.org
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
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.
-
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 *)
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.
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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