|
%I #12 Jan 28 2024 02:41:12
%S 0,0,0,2,6,18,41,94,198,416,853,1746,3531,7151,14415,29049,58431,
%T 117528,236145,474436,952627,1912494,3838175,7701540,15449676,
%U 30988137,62142415,124600422,249795358,500719994,1003575768,2011211100,4030123185,8074898552,16177657763,32408393211,64917907623
%N Number of subsets of {1..n} not containing all of their own first differences.
%F a(n) = 2^n - A364671(n). - _Andrew Howroyd_, Jan 27 2024
%e The a(0) = 0 through a(5) = 18 subsets:
%e . . . {1,3} {1,3} {1,3}
%e {2,3} {1,4} {1,4}
%e {2,3} {1,5}
%e {3,4} {2,3}
%e {1,3,4} {2,5}
%e {2,3,4} {3,4}
%e {3,5}
%e {4,5}
%e {1,2,5}
%e {1,3,4}
%e {1,3,5}
%e {1,4,5}
%e {2,3,4}
%e {2,3,5}
%e {2,4,5}
%e {3,4,5}
%e {1,3,4,5}
%e {2,3,4,5}
%t Table[Length[Select[Subsets[Range[n]],!SubsetQ[#,Differences[#]]&]],{n,0,10}]
%Y For disjunction instead of containment we have A364463, partitions A363260.
%Y For overlap we have A364466, partitions A364467 (strict A364536).
%Y The complement is counted by A364671, partitions A364673, A364674, A364675.
%Y First differences of terms are A364753, complement A364752.
%Y Cf. A007862, A054519, A151897, A237667, A325325, A326083, A363225, A364345, A364464, A364537.
%K nonn
%O 0,4
%A _Gus Wiseman_, Aug 05 2023
%E a(21) onwards (using A364671) added by _Andrew Howroyd_, Jan 27 2024
|
