A363145 - OEIS

%I #17 Jul 15 2023 06:35:23

%S 1,2,4,6,8,12,21,30,38,48,63,91,145,222,390,558,712,892,1142,1456,

%T 1936,2464,3270,4792,7690,11854,18757,28733,47355,73632,130315,186998,

%U 239552,300347,388902,492078,643230,816210,1057438,1354293,1804608,2338124,3111812

%N Number of subsets S of {A007931(1), A007931(2), ..., A007931(n)} with the property that no element of S is a substring of any other.

%C These subsets form an independence system, also called an abstract simplicial complex.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Abstract_simplicial_complex">Abstract simplicial complex</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Independence_system">Independence system</a>

%e For n = 5 the a(5) = 12 independent sets of {A007931(1), A007931(2), ..., A007931(5)} = {1, 2, 11, 12, 21} are:

%e    1) {};

%e    2) {1};

%e    3) {2};

%e    4) {2, 1};

%e    5) {11};

%e    6) {11, 2};

%e    7) {12};

%e    8) {12, 11};

%e    9) {21};

%e   10) {21, 11};

%e   11) {21, 12}; and

%e   12) {21, 12, 11}.

%e In each of these twelve sets, no string is a substring of any other. In particular, {12, 11, 2} is not an independent set because 2 is a substring of 12.

%Y Cf. A007931.

%K nonn,base

%O 0,2

%A _Peter Kagey_, May 19 2023

%E More terms from _Pontus von Brömssen_, Jul 15 2023