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A265332
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a(n) is the index of the column in A265901 where n appears; also the index of the row in A265903 where n appears.
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15
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1, 2, 1, 3, 1, 1, 2, 4, 1, 1, 1, 2, 1, 2, 3, 5, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 6, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 3, 1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5, 7, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 3, 1, 1, 1, 2, 1, 1, 2, 1, 2, 3, 1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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a(1) = 1; for n > 1, a(n) = A051135(n).
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EXAMPLE
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Illustration how the sequence can be constructed by concatenating the frequency counts Q_n of each successive level n of A004001-tree:
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1 Q_0 = (1)
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_2__ Q_1 = (2)
/ \
_3 __4_____ Q_2 = (1,3)
/ / | \
_5 _6 _7 __8___________ Q_3 = (1,1,2,4)
/ / / | / | \ \
_9 10 11 12 13 14 15___ 16_________ Q_4 = (1,1,1,2,1,2,3,5)
/ / / / | / / | |\ \ | \ \ \ \
17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
--
The above illustration copied from the page 229 of Kubo and Vakil paper (page 5 in PDF).
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MATHEMATICA
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terms = 120;
h[1] = 1; h[2] = 1;
h[n_] := h[n] = h[h[n - 1]] + h[n - h[n - 1]];
seq[nmax_] := seq[nmax] = (Length /@ Split[Sort @ Array[h, nmax, 2]])[[;; terms]];
seq[nmax = 2 terms];
seq[nmax += terms];
While[seq[nmax] != seq[nmax - terms], nmax += terms];
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PROG
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CROSSREFS
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Essentially same as A051135 apart from the initial term, which here is set as a(1)=1.
Cf. A162598 (corresponding other index).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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