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

0,2

Comments

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

Links

Table of n, a(n) for n=0..42.

Wikipedia, Abstract simplicial complex

Wikipedia, Independence system

Example

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.

Crossrefs

Cf. A007931.

Sequence in context: A362231 A118563 A228515 * A164145 A354530 A140999

Adjacent sequences: A363142 A363143 A363144 * A363146 A363147 A363148

Keyword

nonn,base

Author

Peter Kagey, May 19 2023

Extensions

More terms from Pontus von Brömssen, Jul 15 2023

Status

approved