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

0,5

Links

Table of n, a(n) for n=0..33.

Index entries for linear recurrences with constant coefficients, signature (4,-3,-6,10,-4).

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)).

Example

The 2 relevant subsets of {1,2,3,4} and {1,2,4} and {1,2,3,4}.

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}]

Crossrefs

Cf. A357284.

Sequence in context: A101696 A155861 A212140 * A136594 A268502 A167826

Adjacent sequences: A357280 A357281 A357282 * A357284 A357285 A357286

Keyword

nonn,easy

Author

Clark Kimberling, Sep 27 2022

Status

approved