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A282168
a(n) is the minimal sum of a positive integer sequence of length n with no duplicate substrings (forward or backward) of length greater than 1.
4
1, 2, 4, 6, 8, 10, 13, 16, 19, 22, 25, 29
OFFSET
1,2
COMMENTS
Examples:
[1,2,3,1,2] is invalid because the substring [1,2] appears twice.
[1,2,1] is invalid because the substring [1,2] appears twice (once forward and once backward).
This sequence is distinct from A025224: a(28) = 102 > A025224(28).
Other known terms:
a(19) = 57;
a(28) = 102;
a(40) = 174;
a(53) = 265.
EXAMPLE
a(1) = 1 via [1];
a(2) = 2 via [1,1];
a(3) = 4 via [1,1,2];
a(4) = 6 via [1,1,2,2];
a(5) = 8 via [1,1,2,3,1];
a(6) = 10 via [1,1,2,2,3,1];
a(7) = 13 via [1,1,2,2,3,3,1];
a(8) = 16 via [1,1,2,2,3,1,4,2];
a(9) = 19 via [1,1,2,2,3,3,1,4,2];
a(10) = 22 via [1,1,2,2,3,1,4,2,5,1];
a(11) = 25 via [1,1,2,2,3,3,1,4,2,5,1];
a(12) = 29 via [1,1,2,2,3,3,1,4,4,2,5,1].
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Peter Kagey, Feb 07 2017
STATUS
approved