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

Author

Gus Wiseman, Jun 04 2019

Keywords

• nonn

Comments

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

Examples

			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}
		

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.

Crossrefs

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

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

Programs

Mathematica

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

Extensions

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