A357289
a(n) = number of subsets S of {1,2,...,n} having more than 2 elements such that (sum of least three elements of S) > max(S).
Original entry on oeis.org
0, 0, 0, 1, 5, 16, 38, 83, 167, 314, 572, 1021, 1757, 3004, 5082, 8439, 13971, 23086, 37576, 61281, 99833, 160912, 259878, 420283, 672847, 1081058, 1739124, 2774021, 4439701, 7121188, 11326386, 18087487, 28944587, 45962070, 73268704, 117090409, 185684721, 295697784, 472033278, 747983491
Offset: 0
The 5 relevant subsets of {1,2,3,4} are {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, and {1, 2, 3, 4}.
-
s[n_] := s[n] = Select[Subsets[Range[n]], Length[#] >= 3 &];
a[n_] := Select[s[n], #[[1]] + #[[2]] + #[[3]] > #[[-1]] &]
Table[Length[a[n]], {n, 0, 16}]
A357291
a(n) = number of subsets S of {1,2,...,n} having more than 2 elements such that (sum of least two elements of S) < difference between greatest two elements of S.
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 1, 3, 8, 19, 42, 89, 185, 378, 766, 1544, 3102, 6220, 12459, 24939, 49902, 99831, 199692, 399417, 798871, 1597782, 3195608, 6391264, 12782580, 25565216, 51130493, 102261051, 204522172, 409044419, 818088918, 1636177921, 3272355933
Offset: 0
The 3 relevant subsets of {1,2,3,4,5,6,7} are {1, 2, 6}, {1, 2, 7}, {1, 2, 3, 7}.
-
s[n_] := s[n] = Select[Subsets[Range[n]], Length[#] >= 3 &];
a[n_] := Select[s[n], #[[1]] + #[[2]] < #[[-1]] - #[[-2]] &]
Table[Length[a[n]], {n, 0, 15}]
A357292
a(n) = number of subsets S of {1,2,...,n} having more than 2 elements such that (sum of least two elements of S) = difference between greatest two elements of S.
Original entry on oeis.org
0, 0, 0, 0, 0, 1, 2, 5, 11, 23, 47, 96, 193, 388, 778, 1558, 3118, 6239, 12480, 24963, 49929, 99861, 199725, 399454, 798911, 1597826, 3195656, 6391316, 12782636, 25565277, 51130558, 102261121, 204522247, 409044499, 818089003, 1636178012, 3272356029
Offset: 0
The 2 relevant subsets of {1,2,3,4,5,6} are {1, 2, 5} and {1,2,3,6}.
-
s[n_] := s[n] = Select[Subsets[Range[n]], Length[#] >= 3 &];
a[n_] := Select[s[n], #[[1]] + #[[2]] == #[[-1]] - #[[-2]] &]
Table[Length[a[n]], {n, 0, 16}]
Showing 1-3 of 3 results.