A357283 a(n) = number of subsets S of {1,2,...,n} having more than 1 element such that (sum of least two elements of S) < max(S).
0, 0, 0, 0, 2, 8, 26, 68, 166, 376, 826, 1756, 3678, 7584, 15522, 31524, 63782, 128552, 258602, 519212, 1041454, 2086960, 4180018, 8368180, 16748598, 33513528, 67051578, 134135868, 268320830, 536707136, 1073512514, 2147156036, 4294508614, 8589279304
Offset: 0
Examples
The 2 relevant subsets of {1,2,3,4} and {1,2,4} and {1,2,3,4}.
Links
- Index entries for linear recurrences with constant coefficients, signature (4,-3,-6,10,-4).
Crossrefs
Cf. A357284.
Programs
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Mathematica
s[n_] := s[n] = Select[Subsets[Range[n]], Length[#] >= 2 &]; (* note size >=2 *) a[n_] := Select[s[n], #[[2]] + #[[1]] < #[[-1]] &] Table[Length[a[n]], {n, 0, 18}]
Formula
a(n) = 4*a(n-1) - 3*a(n-2) - 6*a(n-3) + 10*a(n-4) - 4*a(n-5).
G.f.: (2 x^4)/((-1 + x)^2 (1 - 2 x - 2 x^2 + 4 x^3)).