

A194195


First inverse function (numbers of rows) for pairing function A060734


2



1, 2, 2, 1, 3, 3, 3, 2, 1, 4, 4, 4, 4, 3, 2, 1, 5, 5, 5, 5, 5, 4, 3, 2, 1, 6, 6, 6, 6, 6, 6, 5, 4, 3, 2, 1, 7, 7, 7, 7, 7, 7, 7, 6, 5, 4, 3, 2, 1, 8, 8, 8, 8, 8, 8, 8, 8, 7, 6, 5, 4, 3, 2, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9
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OFFSET

1,2


COMMENTS

The sequence is the second inverse function (numbers of columns) for pairing function A060736.


LINKS

Boris Putievskiy, Rows n = 1..140 of triangle, flattened
Boris Putievskiy, Transformations Integer Sequences And Pairing Functions arXiv:1212.2732 [math.CO], 2012.


FORMULA

a(n) = min{t; t^2  n + 1}, where t=floor(sqrt(n1))+1.


EXAMPLE

The start of the sequence as triangle array read by rows:
1;
2,2,1;
3,3,3,2,1;
4,4,4,4,3,2,1;
. . .
Row number k contains 2k1 numbers k,k,...k,k1,k2,...1 (k times repetition "k").


MATHEMATICA

f[n_]:=Module[{t=Floor[Sqrt[n1]]+1}, Min[t, t^2n+1]]; Array[f, 80] (* Harvey P. Dale, Dec 31 2012 *)


PROG

(Python)
t=int(math.sqrt(n1)) +1
i=min(t, t**2n+1)


CROSSREFS

Cf. A060734, A060736, A220603, A220604
Sequence in context: A097094 A210870 A104726 * A164999 A292030 A162909
Adjacent sequences: A194192 A194193 A194194 * A194196 A194197 A194198


KEYWORD

nonn,tabf


AUTHOR

Boris Putievskiy, Dec 21 2012


STATUS

approved



