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.

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

0,7

Links

Table of n, a(n) for n=0..36.

Index entries for linear recurrences with constant coefficients, signature (2,1,-1,-2,-1,2).

Formula

a(n) = 2*a(n-1) + a(n-2) - a(n-3) - 2*a(n-4) - a(n-5) + 2*a(n-6).

G.f.: -(x^5/((-1 + x)^2 (1 + x) (-1 + 2 x) (1 + x + x^2))).

Example

The 2 relevant subsets of {1,2,3,4,5,6} are {1, 2, 5} and {1,2,3,6}.

Mathematica

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}]

Crossrefs

Cf. A357290, A357291.

Sequence in context: A055010 A266550 A081973 * A334276 A055496 A105120

Adjacent sequences: A357289 A357290 A357291 * A357293 A357294 A357295

Keyword

nonn,easy

Author

Clark Kimberling, Oct 02 2022

Status

approved