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%I A364671 #12 Sep 06 2023 20:30:49
%S A364671 1,2,4,6,10,14,23,34,58,96,171,302,565,1041,1969,3719,7105,13544,
%T A364671 25999,49852,95949,184658,356129,687068,1327540,2566295,4966449,
%U A364671 9617306,18640098,36150918,70166056,136272548,264844111,515036040,1002211421,1951345157,3801569113
%N A364671 Number of subsets of {1..n} containing all of their own first differences.
%H A364671 Rémy Sigrist, <a href="/A364671/a364671.txt">C++ program</a>
%e A364671 The subset {1,2,4,5,10,14} has differences (1,2,1,5,4) so is counted under a(14).
%e A364671 The a(0) = 1 through a(5) = 14 subsets:
%e A364671   {}  {}   {}     {}       {}         {}
%e A364671       {1}  {1}    {1}      {1}        {1}
%e A364671            {2}    {2}      {2}        {2}
%e A364671            {1,2}  {3}      {3}        {3}
%e A364671                   {1,2}    {4}        {4}
%e A364671                   {1,2,3}  {1,2}      {5}
%e A364671                            {2,4}      {1,2}
%e A364671                            {1,2,3}    {2,4}
%e A364671                            {1,2,4}    {1,2,3}
%e A364671                            {1,2,3,4}  {1,2,4}
%e A364671                                       {1,2,3,4}
%e A364671                                       {1,2,3,5}
%e A364671                                       {1,2,4,5}
%e A364671                                       {1,2,3,4,5}
%t A364671 Table[Length[Select[Subsets[Range[n]], SubsetQ[#,Differences[#]]&]], {n,0,10}]
%o A364671 (C++) See Links section.
%Y A364671 For differences of all strict pairs we have A054519, for partitions A007862.
%Y A364671 For "disjoint" instead of "subset" we have A364463, partitions A363260.
%Y A364671 For "non-disjoint" we have A364466, partitions A364467 (strict A364536).
%Y A364671 The complement is counted by A364672, partitions A364673, A364674, A364675.
%Y A364671 First differences of terms are A364752, complement A364753.
%Y A364671 Cf. A151897, A196723, A237667, A237668, A325325, A326083, A363225, A364345, A364464, A364537.
%K A364671 nonn
%O A364671 0,2
%A A364671 _Gus Wiseman_, Aug 04 2023
%E A364671 More terms from _Rémy Sigrist_, Aug 06 2023

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