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A329985
a(1) = 1 and for n > 0, a(n+1) = a(k) - a(n) where k is the number of terms equal to a(n) among the first n terms.
8
1, 0, 1, -1, 2, -1, 1, 0, 0, 1, -2, 3, -2, 2, -2, 3, -3, 4, -3, 3, -2, 1, 1, -2, 4, -4, 5, -4, 4, -3, 4, -5, 6, -5, 5, -5, 6, -6, 7, -6, 6, -5, 4, -2, 1, 0, -1, 2, -1, 0, 2, -3, 2, 0, -1, 3, -4, 5, -4, 3, -1, 0, 1, -1, 2, -3, 5, -6, 7, -7, 8, -7, 7, -6, 5, -3
OFFSET
1,5
COMMENTS
In other words, for n > 0, a(n+1) = a(o(n)) - a(n) where o is the ordinal transform of the sequence.
The sequence has interesting graphical features (see plot in Links section).
LINKS
N. J. A. Sloane (in collaboration with Scott R. Shannon), Art and Sequences, Slides of guest lecture in Math 640, Rutgers Univ., Feb 8, 2020. Mentions this sequence.
EXAMPLE
The first terms, alongside their ordinal transform, are:
n a(n) o(n)
-- ---- ----
1 1 1
2 0 1
3 1 2
4 -1 1
5 2 1
6 -1 2
7 1 3
8 0 2
9 0 3
10 1 4
MATHEMATICA
A={1}; For[n=2, n<=76, n++, A=Append[A, Part[A, Count[Table[Part[A, i], {i, 1, n-1}], Part[A, n-1]]]-Part[A, n-1]]]; A (* Joshua Oliver, Nov 26 2019 *)
Nest[Append[#, #[[Count[#, #[[-1]] ] ]] - #[[-1]]] &, {1}, 75] (* Michael De Vlieger, Dec 01 2019 *)
PROG
(PARI) for (n=1, #(a=vector(76)), print1 (a[n]=if (n==1, 1, a[sum(k=1, n-1, a[k]==a[n-1])]-a[n-1])", "))
CROSSREFS
o(n) is A330334.
See A329981 for similar sequences.
Sequence in context: A277349 A078807 A208249 * A029422 A351356 A152800
KEYWORD
sign,look
AUTHOR
Rémy Sigrist, Nov 26 2019
STATUS
approved