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A326175 Number of minimal subsets of {1..n} containing n whose sum is greater than or equal to the sum of their complement. 6
1, 1, 1, 3, 3, 5, 10, 14, 25, 44, 71, 128, 231, 411, 740, 1352, 2481, 4570, 8390, 15550, 29103, 54345, 101312, 190316, 359827, 679051, 1279956, 2426200, 4621174, 8789565, 16701225, 31871629, 61052515, 116818123, 223333533, 428435056, 824395640, 1584833707, 3044562148, 5865073390, 11326741619, 21857561924 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Table of n, a(n) for n=1..42.

EXAMPLE

The a(1) = 1 through a(8) = 14 subsets:

  {1}  {2}  {3}  {1,4}  {3,5}    {5,6}    {1,6,7}    {3,7,8}

                 {2,4}  {4,5}    {1,4,6}  {2,5,7}    {4,6,8}

                 {3,4}  {1,2,5}  {2,3,6}  {2,6,7}    {4,7,8}

                                 {2,4,6}  {3,4,7}    {5,6,8}

                                 {3,4,6}  {3,5,7}    {5,7,8}

                                          {3,6,7}    {6,7,8}

                                          {4,5,7}    {1,2,7,8}

                                          {4,6,7}    {1,3,6,8}

                                          {5,6,7}    {1,4,5,8}

                                          {1,2,4,7}  {2,3,5,8}

                                                     {2,3,6,8}

                                                     {2,4,5,8}

                                                     {3,4,5,8}

                                                     {1,2,3,4,8}

MATHEMATICA

fasmin[y_]:=Complement[y, Union@@Table[Union[s, #]&/@Rest[Subsets[Complement[Union@@y, s]]], {s, y}]];

Table[Length[fasmin[Select[Subsets[Range[n]], MemberQ[#, n]&&Plus@@#>=Plus@@Complement[Range[n], #]&]]], {n, 10}]

CROSSREFS

Cf. A053632, A057567, A057568, A059529, A063865, A326152, A326173, A326174.

Sequence in context: A294617 A320450 A100886 * A072337 A335056 A132751

Adjacent sequences:  A326172 A326173 A326174 * A326176 A326177 A326178

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 11 2019

EXTENSIONS

a(15)-a(42) from Bert Dobbelaere, Jun 22 2019

STATUS

approved

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Last modified September 19 07:08 EDT 2021. Contains 347554 sequences. (Running on oeis4.)