

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
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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

The complement is counted by A364752.
A054519 counts subsets containing differences, A326083 containing sums.


KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



