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.
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].
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].
Showing 1-4 of 4 results.