cp's OEIS Frontend

A363145 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.

%I A363145 #17 Jul 15 2023 06:35:23
%S A363145 1,2,4,6,8,12,21,30,38,48,63,91,145,222,390,558,712,892,1142,1456,
%T A363145 1936,2464,3270,4792,7690,11854,18757,28733,47355,73632,130315,186998,
%U A363145 239552,300347,388902,492078,643230,816210,1057438,1354293,1804608,2338124,3111812
%N A363145 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 A363145 These subsets form an independence system, also called an abstract simplicial complex.
%H A363145 Wikipedia, <a href="https://en.wikipedia.org/wiki/Abstract_simplicial_complex">Abstract simplicial complex</a>
%H A363145 Wikipedia, <a href="https://en.wikipedia.org/wiki/Independence_system">Independence system</a>
%e A363145 For n = 5 the a(5) = 12 independent sets of {A007931(1), A007931(2), ..., A007931(5)} = {1, 2, 11, 12, 21} are:
%e A363145    1) {};
%e A363145    2) {1};
%e A363145    3) {2};
%e A363145    4) {2, 1};
%e A363145    5) {11};
%e A363145    6) {11, 2};
%e A363145    7) {12};
%e A363145    8) {12, 11};
%e A363145    9) {21};
%e A363145   10) {21, 11};
%e A363145   11) {21, 12}; and
%e A363145   12) {21, 12, 11}.
%e A363145 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 A363145 Cf. A007931.
%K A363145 nonn,base
%O A363145 0,2
%A A363145 _Peter Kagey_, May 19 2023
%E A363145 More terms from _Pontus von Brömssen_, Jul 15 2023