

A100037


Positions of occurrences of the natural numbers as a second subsequence in A100035.


21



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

1,1


COMMENTS

For n > 1, A100035(a(n)) = n and A100035(m) != n for a(n1) <= m < a(n);
A100036(n) < a(n) < A100038(n) < A100039(n).


LINKS

Table of n, a(n) for n=1..48.
GuoNiu Han, Enumeration of Standard Puzzles, 2011. [Cached copy]
GuoNiu Han, Enumeration of Standard Puzzles, arXiv:2006.14070 [math.CO], 2020.


FORMULA

a(n) = 2*n^2  n + 3 (conjectured).  Ralf Stephan, May 15 2007


EXAMPLE

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.


CROSSREFS

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


KEYWORD

nonn


AUTHOR

Reinhard Zumkeller, Oct 31 2004


STATUS

approved



