A364671 - OEIS

%I #12 Sep 06 2023 20:30:49

%S 1,2,4,6,10,14,23,34,58,96,171,302,565,1041,1969,3719,7105,13544,

%T 25999,49852,95949,184658,356129,687068,1327540,2566295,4966449,

%U 9617306,18640098,36150918,70166056,136272548,264844111,515036040,1002211421,1951345157,3801569113

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

%H Rémy Sigrist, <a href="/A364671/a364671.txt">C++ program</a>

%e The subset {1,2,4,5,10,14} has differences (1,2,1,5,4) so is counted under a(14).

%e The a(0) = 1 through a(5) = 14 subsets:

%e   {}  {}   {}     {}       {}         {}

%e       {1}  {1}    {1}      {1}        {1}

%e            {2}    {2}      {2}        {2}

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

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

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

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

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

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

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

%e                                       {1,2,3,4}

%e                                       {1,2,3,5}

%e                                       {1,2,4,5}

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

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

%o (C++) See Links section.

%Y For differences of all strict pairs we have A054519, for partitions A007862.

%Y For "disjoint" instead of "subset" we have A364463, partitions A363260.

%Y For "non-disjoint" we have A364466, partitions A364467 (strict A364536).

%Y The complement is counted by A364672, partitions A364673, A364674, A364675.

%Y First differences of terms are A364752, complement A364753.

%Y Cf. A151897, A196723, A237667, A237668, A325325, A326083, A363225, A364345, A364464, A364537.

%K nonn

%O 0,2

%A _Gus Wiseman_, Aug 04 2023

%E More terms from _Rémy Sigrist_, Aug 06 2023