A357282 a(n) = number of subsets S of {1,2,...,n} having more than 1 element such that (difference between least two elements of S) = difference between greatest two elements of S.

0, 0, 1, 4, 9, 18, 33, 60, 109, 202, 381, 732, 1425, 2802, 5545, 11020, 21957, 43818, 87525, 174924, 349705, 699250, 1398321, 2796444, 5592669, 11185098, 22369933, 44739580, 89478849, 178957362, 357914361, 715828332, 1431656245, 2863312042, 5726623605

Offset

0,4

Links

Table of n, a(n) for n=0..34.

Index entries for linear recurrences with constant coefficients, signature (4,-4,-2,5,-2)

Formula

a(n) = A000295(n)-2*A272144(n-2) for n >= 2.

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

G.f.: -((x^2 (-1 + 3 x^2))/((-1 + x)^3 (1 + x) (-1 + 2 x))).

Example

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

Mathematica

s[n_] := s[n] = Select[Subsets[Range[n]], Length[#] >= 2 &];
a[n_] := Select[s[n], #[[2]] - #[[1]] == #[[-1]] - #[[-2]] &];
Table[Length[a[n]], {n, 0, 18}]

Crossrefs

Cf. A000295, A272144.

Sequence in context: A192760 A295964 A292765 * A301157 A019454 A019453

Adjacent sequences: A357279 A357280 A357281 * A357283 A357284 A357285

Keyword

nonn,easy

Author

Clark Kimberling, Sep 27 2022

Status

approved