A326021 Number of complete subsets of {1..n} with maximum n.

1, 1, 1, 2, 3, 6, 12, 23, 45, 90, 180, 359, 717, 1432, 2862, 5723, 11444, 22887, 45772, 91541, 183078, 366151, 732295, 1464583, 2929158, 5858307, 11716603, 23433196, 46866379, 93732744, 187465471, 374930922, 749861819, 1499723610

Offset

1,4

Comments

A set of positive integers summing to n is complete if every nonnegative integer up to n is the sum of some subset.

Links

Charlie Neder, Table of n, a(n) for n = 1..300

Andrzej Kukla and Piotr Miska, On practical sets and A-practical numbers, arXiv:2405.18225 [math.NT], 2024.

Example

The a(1) = 1 through a(7) = 12 subsets:
  {1}  {1,2}  {1,2,3}  {1,2,4}    {1,2,3,5}    {1,2,3,6}      {1,2,3,7}
                       {1,2,3,4}  {1,2,4,5}    {1,2,4,6}      {1,2,4,7}
                                  {1,2,3,4,5}  {1,2,3,4,6}    {1,2,3,4,7}
                                               {1,2,3,5,6}    {1,2,3,5,7}
                                               {1,2,4,5,6}    {1,2,3,6,7}
                                               {1,2,3,4,5,6}  {1,2,4,5,7}
                                                              {1,2,4,6,7}
                                                              {1,2,3,4,5,7}
                                                              {1,2,3,4,6,7}
                                                              {1,2,3,5,6,7}
                                                              {1,2,4,5,6,7}
                                                              {1,2,3,4,5,6,7}

Mathematica

Table[Length[Select[Subsets[Range[n]], Max@@#==n&&Union[Plus@@@Subsets[#]]==Range[0, Total[#]]&]], {n, 10}]

Crossrefs

Cf. A002033, A103295, A108917, A126796, A188431, A276024.

Cf. A325684, A325781, A325790, A325791, A325986, A325988, A326016, A326020, A326022, A326036.

Sequence in context: A338218 A001630 A293363 * A164363 A306809 A103341

Adjacent sequences: A326018 A326019 A326020 * A326022 A326023 A326024

Keyword

nonn

Author

Gus Wiseman, Jun 04 2019

Extensions

a(18)-a(34) from Charlie Neder, Jun 05 2019

Status

approved