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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).
2
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
0,4
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
FORMULA
See the formulas in A350102.
a(n) = 2^n - A350102(n).
PROG
(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))
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Dec 16 2021
STATUS
approved