|
%I #11 Mar 10 2017 21:32:37
%S 1,1,3,2,2,6,6,48,60,168,144,288,1872
%N The number of positive integer sequences of length n with no duplicate substrings and a minimal sum (i.e., the sum of the sequence is A259280(n)).
%e For n = 7 the a(7) = 6 sequences are
%e 1,3,1,2,2,1,1;
%e 1,2,2,1,3,1,1;
%e 1,3,1,1,2,2,1;
%e 1,1,3,1,2,2,1;
%e 1,2,2,1,1,3,1; and
%e 1,1,2,2,1,3,1.
%t 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 *)
%Y Cf. A259280. A283557 is the product analog.
%K nonn,more
%O 1,3
%A _Peter Kagey_, Mar 10 2017
%E a(11)-a(13) from _Giovanni Resta_, Mar 10 2017
|
