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].
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 *)
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].
A284433
The number of positive integer sequences of length n with no duplicate substrings (forward or backward) of length greater than 1, every number different from its neighbors, and a minimal sum (= A282167(n)).
Original entry on oeis.org
1, 2, 6, 2, 18, 12, 24, 24, 1320, 240, 528, 720, 5664, 105888, 16992, 150048, 244800, 4266432, 4375296, 39598848, 50637312, 123310080, 202549248, 15925690368, 3765657600, 23454351360, 101739110400, 437749678080, 1572538613760, 11891771080704, 7862693068800, 185042766200832
Offset: 1
For n = 4 the a(4) = 2 solutions are [1,3,2,1] and [1,2,3,1].
Showing 1-4 of 4 results.