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A283558
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)).
1
1, 1, 3, 2, 2, 6, 6, 48, 60, 168, 144, 288, 1872
OFFSET
1,3
EXAMPLE
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.
MATHEMATICA
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 *)
CROSSREFS
Cf. A259280. A283557 is the product analog.
Sequence in context: A197586 A111702 A283557 * A234713 A091029 A272372
KEYWORD
nonn,more
AUTHOR
Peter Kagey, Mar 10 2017
EXTENSIONS
a(11)-a(13) from Giovanni Resta, Mar 10 2017
STATUS
approved