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.

1, 2, 4, 6, 8, 10, 13, 16, 19, 22, 25, 29, 33, 37, 41, 45, 49, 53, 57, 62, 67, 72, 77, 82, 87, 92, 97, 102, 108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 174, 181, 188, 195, 202, 209, 216, 223, 230, 237, 244, 251, 258, 265, 273, 281, 289, 297, 305, 313, 321, 329, 337, 345, 353

Offset: 1

Author

Peter Kagey, Feb 07 2017

Keywords

• nonn

Comments

This sequence shares first 12 terms with A025224, but then they diverge: a(13) = 33 > 32 = A025224(13).

We seem to have a(n) = a(n-1) + a(n-2) - a(n-3) + d(n), where d(n) is 0 or 1. Compare to A282166. - Max Alekseyev, Jun 13 2025

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).
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

Cf. A259280, A282166, A282167, A282193.

Extensions

Edited and terms a(13) onward added by Max Alekseyev, Feb 05 2025