A364465 - OEIS

%I #12 Oct 18 2023 04:52:04

%S 1,2,4,7,13,22,36,61,99,156,240,381,587,894,1334,1967,2951,4370,6406,

%T 9293,13357,18976,27346,39013,55437,78154,109632,152415,210801,293502,

%U 406664,561693,772463,1058108,1441796,1956293,2639215,3579542,4835842,6523207

%N Number of subsets of {1..n} with all different first differences of elements.

%H Rémy Sigrist, <a href="/A364465/a364465.txt">C++ program</a>

%e The a(0) = 1 through a(4) = 13 subsets:

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

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

%e            {2}    {2}    {2}

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

%e                   {1,2}  {4}

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

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

%e                          {1,4}

%e                          {2,3}

%e                          {2,4}

%e                          {3,4}

%e                          {1,2,4}

%e                          {1,3,4}

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

%Y For all differences of pairs of elements we have A196723

%Y For partitions instead of subsets we have A325325, strict A320347.

%Y For subset-sums we have A325864, for partitions A108917, A275972.

%Y A007318 counts subsets by length.

%Y A053632 counts subsets by sum.

%Y A363260 counts partitions disjoint from differences, complement A364467.

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

%Y Cf. A000009, A008289, A011782, A236912, A320348, A325857, A325877, A325878, A326083, A364345, A364346.

%K nonn

%O 0,2

%A _Gus Wiseman_, Jul 30 2023

%E More terms from _Rémy Sigrist_, Aug 06 2023