A350105 Number of subsets of the initial segment of the natural numbers strictly below n which are not self-measuring. Number of subsets S of [n] with S != distset(S).

0, 0, 1, 3, 9, 22, 52, 112, 238, 490, 999, 2019, 4065, 8155, 16345, 32725, 65489, 131020, 262090, 524228, 1048514, 2097084, 4194232, 8388532, 16777138, 33554346, 67108775, 134217635, 268435359, 536870809, 1073741719, 2147483535, 4294967181, 8589934471, 17179869059

Offset: 0

Author

Peter Luschny, Dec 16 2021

Keywords

• nonn

Comments

We use the notation [n] = {0, 1, ..., n-1}. If S is a subset of [n] then we define the distset of S (set of distances of S) as {|x - y|: x, y in S}. We call a subset S of the natural numbers self-measuring if and only if S = distset(S).

Links

• Winston de Greef, Table of n, a(n) for n = 0..3305

Crossrefs

Cf. A350102, A350103, A349976.

Programs

SageMath

def A350105List(len):
    L = [0] * len
    b, z = 2, 2
    for n in (2..len-1):
        b += sloane.A000005(n - 1)
        z += z
        L[n] = z - b
    return L
print(A350105List(35))

Formula

See the formulas in A350102.

a(n) = 2^n - A350102(n).