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.

1, 2, 4, 6, 8, 12, 21, 30, 38, 48, 63, 91, 145, 222, 390, 558, 712, 892, 1142, 1456, 1936, 2464, 3270, 4792, 7690, 11854, 18757, 28733, 47355, 73632, 130315, 186998, 239552, 300347, 388902, 492078, 643230, 816210, 1057438, 1354293, 1804608, 2338124, 3111812

Offset: 0

Author

Peter Kagey, May 19 2023

Keywords

• nonn
• base

Comments

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

Examples

			For n = 5 the a(5) = 12 independent sets of {A007931(1), A007931(2), ..., A007931(5)} = {1, 2, 11, 12, 21} are:
   1) {};
   2) {1};
   3) {2};
   4) {2, 1};
   5) {11};
   6) {11, 2};
   7) {12};
   8) {12, 11};
   9) {21};
  10) {21, 11};
  11) {21, 12}; and
  12) {21, 12, 11}.
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.
		

Links

• Wikipedia, Abstract simplicial complex
• Wikipedia, Independence system

Crossrefs

Cf. A007931.

Extensions

More terms from Pontus von Brömssen, Jul 15 2023