A364752 - OEIS

%I #11 Aug 06 2023 17:50:09

%S 1,1,2,2,4,4,9,11,24,38,75,131,263,476,928,1750,3386,6439,12455,23853,

%T 46097,88709,171471,330939,640472,1238755,2400154,4650857,9022792,

%U 17510820,34015138,66106492,128571563,250191929,487175381,949133736,1850223956,3608650389

%N Number of subsets of {1..n} containing n and all first differences.

%H Rémy Sigrist, <a href="/A364752/a364752.txt">C++ program</a>

%e The a(1) = 1 through a(6) = 9 subsets:

%e   {1}  {2}    {3}      {4}        {5}          {6}

%e        {1,2}  {1,2,3}  {2,4}      {1,2,3,5}    {3,6}

%e                        {1,2,4}    {1,2,4,5}    {2,4,6}

%e                        {1,2,3,4}  {1,2,3,4,5}  {1,2,3,6}

%e                                                {1,2,4,6}

%e                                                {1,2,3,4,6}

%e                                                {1,2,3,5,6}

%e                                                {1,2,4,5,6}

%e                                                {1,2,3,4,5,6}

%t Table[If[n==0,1,Length[Select[Subsets[Range[n]], MemberQ[#,n]&&SubsetQ[#,Differences[#]]&]]],{n,0,10}]

%Y Partial sums are A364671, complement A364672.

%Y The complement is counted by A364753.

%Y A054519 counts subsets containing differences, A326083 containing sums.

%Y A364463 counts subsets disjoint from differences, complement A364466.

%Y A364673 counts partitions containing differences, A364674, A364675.

%Y Cf. A151897, A196723, A237668, A325325, A363225, A364345, A364464, A364537.

%K nonn

%O 0,3

%A _Gus Wiseman_, Aug 06 2023

%E More terms from _Rémy Sigrist_, Aug 06 2023