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A364753 Number of subsets of {1..n} containing n but not containing all first differences. 3
0, 0, 0, 2, 4, 12, 23, 53, 104, 218, 437, 893, 1785, 3620, 7264, 14634, 29382, 59097, 118617, 238291, 478191, 959867, 1925681, 3863365, 7748136, 15538461, 31154278, 62458007, 125194936, 250924636, 502855774, 1007635332, 2018912085, 4044775367, 8102759211, 16230735448, 32509514412, 65110826347 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
In other words, subsets containing both n and some element that is not the difference of two consecutive elements.
LINKS
EXAMPLE
The a(1) = 0 through a(6) = 23 subsets:
. . {1,3} {1,4} {1,5} {1,6}
{2,3} {3,4} {2,5} {2,6}
{1,3,4} {3,5} {4,6}
{2,3,4} {4,5} {5,6}
{1,2,5} {1,2,6}
{1,3,5} {1,3,6}
{1,4,5} {1,4,6}
{2,3,5} {1,5,6}
{2,4,5} {2,3,6}
{3,4,5} {2,5,6}
{1,3,4,5} {3,4,6}
{2,3,4,5} {3,5,6}
{4,5,6}
{1,2,5,6}
{1,3,4,6}
{1,3,5,6}
{1,4,5,6}
{2,3,4,6}
{2,3,5,6}
{2,4,5,6}
{3,4,5,6}
{1,3,4,5,6}
{2,3,4,5,6}
MATHEMATICA
Table[Length[Select[Subsets[Range[n]], MemberQ[#, n]&&!SubsetQ[#, Differences[#]]&]], {n, 0, 10}]
CROSSREFS
Partial sums are A364672, complement A364671.
The complement is counted by A364752.
A054519 counts subsets containing differences, A326083 containing sums.
A364463 counts subsets disjoint from differences, complement A364466.
A364673, A364674, A364675 count partitions containing differences.
Sequence in context: A303030 A291404 A295954 * A052416 A059322 A163908
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 06 2023
EXTENSIONS
More terms from Giorgos Kalogeropoulos, Aug 07 2023
STATUS
approved

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Last modified March 5 02:31 EST 2024. Contains 370537 sequences. (Running on oeis4.)