cp's OEIS Frontend

A366320 Irregular triangle read by rows where T(n,k) is the number of subsets of {1..n} without a subset summing to k.

%I A366320 #9 Oct 13 2023 11:47:13
%S A366320 1,2,2,3,4,4,3,6,6,7,8,8,6,6,9,11,11,14,14,15,16,16,12,12,9,17,17,20,
%T A366320 20,24,27,27,30,30,31,32,32,24,24,18,17,26,31,29,35,36,43,47,50,51,56,
%U A366320 59,59,62,62,63
%N A366320 Irregular triangle read by rows where T(n,k) is the number of subsets of {1..n} without a subset summing to k.
%e A366320 Triangle begins:
%e A366320    1
%e A366320    2  2  3
%e A366320    4  4  3  6  6  7
%e A366320    8  8  6  6  9 11 11 14 14 15
%e A366320   16 16 12 12  9 17 17 20 20 24 27 27 30 30 31
%e A366320   32 32 24 24 18 17 26 31 29 35 36 43 47 50 51 56 59 59 62 62 63
%e A366320 Row n = 3 counts the following subsets:
%e A366320   {}     {}     {}   {}     {}     {}
%e A366320   {2}    {1}    {1}  {1}    {1}    {1}
%e A366320   {3}    {3}    {2}  {2}    {2}    {2}
%e A366320   {2,3}  {1,3}       {3}    {3}    {3}
%e A366320                      {1,2}  {1,2}  {1,2}
%e A366320                      {2,3}  {1,3}  {1,3}
%e A366320                                    {2,3}
%t A366320 Table[Length[Select[Subsets[Range[n]],FreeQ[Total/@Subsets[#],k]&]],{n,8},{k,n*(n+1)/2}]
%Y A366320 Row lengths are A000217.
%Y A366320 The diagonal T(n,n) is A365377, complement A365376.
%Y A366320 The complement is counted by A365381.
%Y A366320 A000009 counts subsets summing to n.
%Y A366320 A000124 counts distinct possible sums of subsets of {1..n}.
%Y A366320 A124506 counts combination-free subsets, differences of A326083.
%Y A366320 A365046 counts combination-full subsets, differences of A364914.
%Y A366320 Cf. A007865, A085489, A093971, A103580, A151897, A326080, A364534, A365073, A365380.
%K A366320 nonn,tabf
%O A366320 1,2
%A A366320 _Gus Wiseman_, Oct 12 2023