cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A326021 #16 Jun 03 2024 13:17:54
%S A326021 1,1,1,2,3,6,12,23,45,90,180,359,717,1432,2862,5723,11444,22887,45772,
%T A326021 91541,183078,366151,732295,1464583,2929158,5858307,11716603,23433196,
%U A326021 46866379,93732744,187465471,374930922,749861819,1499723610
%N A326021 Number of complete subsets of {1..n} with maximum n.
%C A326021 A set of positive integers summing to n is complete if every nonnegative integer up to n is the sum of some subset.
%H A326021 Charlie Neder, <a href="/A326021/b326021.txt">Table of n, a(n) for n = 1..300</a>
%H A326021 Andrzej Kukla and Piotr Miska, <a href="https://arxiv.org/abs/2405.18225">On practical sets and A-practical numbers</a>, arXiv:2405.18225 [math.NT], 2024.
%e A326021 The a(1) = 1 through a(7) = 12 subsets:
%e A326021   {1}  {1,2}  {1,2,3}  {1,2,4}    {1,2,3,5}    {1,2,3,6}      {1,2,3,7}
%e A326021                        {1,2,3,4}  {1,2,4,5}    {1,2,4,6}      {1,2,4,7}
%e A326021                                   {1,2,3,4,5}  {1,2,3,4,6}    {1,2,3,4,7}
%e A326021                                                {1,2,3,5,6}    {1,2,3,5,7}
%e A326021                                                {1,2,4,5,6}    {1,2,3,6,7}
%e A326021                                                {1,2,3,4,5,6}  {1,2,4,5,7}
%e A326021                                                               {1,2,4,6,7}
%e A326021                                                               {1,2,3,4,5,7}
%e A326021                                                               {1,2,3,4,6,7}
%e A326021                                                               {1,2,3,5,6,7}
%e A326021                                                               {1,2,4,5,6,7}
%e A326021                                                               {1,2,3,4,5,6,7}
%t A326021 Table[Length[Select[Subsets[Range[n]],Max@@#==n&&Union[Plus@@@Subsets[#]]==Range[0,Total[#]]&]],{n,10}]
%Y A326021 Cf. A002033, A103295, A108917, A126796, A188431, A276024.
%Y A326021 Cf. A325684, A325781, A325790, A325791, A325986, A325988, A326016, A326020, A326022, A326036.
%K A326021 nonn
%O A326021 1,4
%A A326021 _Gus Wiseman_, Jun 04 2019
%E A326021 a(18)-a(34) from _Charlie Neder_, Jun 05 2019