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A100037
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Positions of occurrences of the natural numbers as a second subsequence in A100035.
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21
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4, 9, 18, 31, 48, 69, 94, 123, 156, 193, 234, 279, 328, 381, 438, 499, 564, 633, 706, 783, 864, 949, 1038, 1131, 1228, 1329, 1434, 1543, 1656, 1773, 1894, 2019, 2148, 2281, 2418, 2559, 2704, 2853, 3006, 3163, 3324, 3489, 3658, 3831, 4008, 4189, 4374, 4563
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OFFSET
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1,1
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COMMENTS
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For n > 1, A100035(a(n)) = n and A100035(m) != n for a(n-1) <= m < a(n);
A100036(n) < a(n) < A100038(n) < A100039(n).
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LINKS
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Table of n, a(n) for n=1..48.
Guo-Niu Han, Enumeration of Standard Puzzles, 2011. [Cached copy]
Guo-Niu Han, Enumeration of Standard Puzzles, arXiv:2006.14070 [math.CO], 2020.
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FORMULA
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a(n) = 2*n^2 - n + 3 (conjectured). - Ralf Stephan, May 15 2007
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EXAMPLE
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First terms (10 = A, 11 = B, 12 = C) of A100035(a(n)):
...1....2........3............4................5......
1231435425165764736271879869584938291A9BA8B7A6B5A4B3A2B;
a(1) = A084849(2) = 4, A100035(4) = 1;
a(2) = A014107(2) = 9, A100035(9) = 2;
a(3) = A033537(3) = 18, A100035(18) = 3;
a(4) = A100040(4) = 31, A100035(31) = 4;
a(5) = A100041(5) = 48, A100035(48) = 5.
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CROSSREFS
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Cf. A014107, A033537, A084849, A100035, A100036, A100038, A100039, A100040, A100041.
Sequence in context: A301017 A008219 A008223 * A063916 A009855 A038402
Adjacent sequences: A100034 A100035 A100036 * A100038 A100039 A100040
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller, Oct 31 2004
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STATUS
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approved
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