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A364672
Number of subsets of {1..n} not containing all of their own first differences.
6
0, 0, 0, 2, 6, 18, 41, 94, 198, 416, 853, 1746, 3531, 7151, 14415, 29049, 58431, 117528, 236145, 474436, 952627, 1912494, 3838175, 7701540, 15449676, 30988137, 62142415, 124600422, 249795358, 500719994, 1003575768, 2011211100, 4030123185, 8074898552, 16177657763, 32408393211, 64917907623
OFFSET
0,4
FORMULA
a(n) = 2^n - A364671(n). - Andrew Howroyd, Jan 27 2024
EXAMPLE
The a(0) = 0 through a(5) = 18 subsets:
. . . {1,3} {1,3} {1,3}
{2,3} {1,4} {1,4}
{2,3} {1,5}
{3,4} {2,3}
{1,3,4} {2,5}
{2,3,4} {3,4}
{3,5}
{4,5}
{1,2,5}
{1,3,4}
{1,3,5}
{1,4,5}
{2,3,4}
{2,3,5}
{2,4,5}
{3,4,5}
{1,3,4,5}
{2,3,4,5}
MATHEMATICA
Table[Length[Select[Subsets[Range[n]], !SubsetQ[#, Differences[#]]&]], {n, 0, 10}]
CROSSREFS
For disjunction instead of containment we have A364463, partitions A363260.
For overlap we have A364466, partitions A364467 (strict A364536).
The complement is counted by A364671, partitions A364673, A364674, A364675.
First differences of terms are A364753, complement A364752.
Sequence in context: A339149 A101695 A376739 * A014741 A016059 A291519
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 05 2023
EXTENSIONS
a(21) onwards (using A364671) added by Andrew Howroyd, Jan 27 2024
STATUS
approved