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 A326573 Number of connected antichains of subsets of {1..n}, all having different sums. 5
 1, 1, 1, 5, 59, 2689, 787382 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS An antichain is a finite set of finite sets, none of which is a subset of any other. It is covering if its union is {1..n}. The edge-sums are the sums of vertices in each edge, so for example the edge sums of {{1,3},{2,5},{3,4,5}} are {4,7,12}. LINKS EXAMPLE The a(3) = 5 antichains:   {{1,2,3}}   {{1,3},{2,3}}   {{1,2},{2,3}}   {{1,2},{1,3}}   {{1,2},{1,3},{2,3}} The a(4) = 59 antichains:   {1234}  {12}{134}   {12}{13}{14}   {12}{13}{14}{24}   {12}{13}{14}{24}{34}           {12}{234}   {12}{13}{24}   {12}{13}{14}{34}   {12}{13}{23}{24}{34}           {13}{124}   {12}{13}{34}   {12}{13}{23}{24}           {13}{234}   {12}{14}{34}   {12}{13}{23}{34}           {14}{123}   {12}{23}{24}   {12}{13}{24}{34}           {14}{234}   {12}{23}{34}   {12}{14}{24}{34}           {23}{124}   {12}{24}{34}   {12}{23}{24}{34}           {23}{134}   {13}{14}{24}   {13}{14}{24}{34}           {24}{134}   {13}{23}{24}   {13}{23}{24}{34}           {34}{123}   {13}{23}{34}   {12}{13}{14}{234}           {123}{124}  {13}{24}{34}   {12}{23}{24}{134}           {123}{134}  {14}{24}{34}   {123}{124}{134}{234}           {123}{234}  {12}{13}{234}           {124}{134}  {12}{14}{234}           {124}{234}  {12}{23}{134}           {134}{234}  {12}{24}{134}                       {13}{14}{234}                       {13}{23}{124}                       {14}{34}{123}                       {23}{24}{134}                       {12}{134}{234}                       {13}{124}{234}                       {14}{123}{234}                       {23}{124}{134}                       {123}{124}{134}                       {123}{124}{234}                       {123}{134}{234}                       {124}{134}{234} CROSSREFS Antichain covers are A006126. Connected antichains are A048143. Set partitions with different block-sums are A275780. MM-numbers of multiset partitions with different part-sums are A326535. Antichain covers with equal edge-sums are A326566. The non-connected case is A326572. Cf. A000372, A293510, A307249, A321469, A323818, A326519, A326565, A326569, A326570, A326571. Sequence in context: A249519 A001059 A290702 * A324240 A120608 A143766 Adjacent sequences:  A326570 A326571 A326572 * A326574 A326575 A326576 KEYWORD nonn,more AUTHOR Gus Wiseman, Jul 18 2019 STATUS approved

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Last modified November 27 06:33 EST 2020. Contains 338678 sequences. (Running on oeis4.)