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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.
0
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.
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
KEYWORD
nonn,base
AUTHOR
Peter Kagey, May 19 2023
EXTENSIONS
More terms from Pontus von Brömssen, Jul 15 2023
STATUS
approved