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A220603 First inverse function (numbers of rows) for pairing function A081344. 6
1, 2, 2, 1, 1, 2, 3, 3, 3, 4, 4, 4, 4, 3, 2, 1, 1, 2, 3, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 7, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Boris Putievskiy, Transformations Integer Sequences And Pairing Functions, arXiv:1212.2732 [math.CO], 2012.
FORMULA
As a linear array, the sequence is a(n) = mod(t;2)*min{t; n - (t - 1)^2} + mod(t + 1; 2)*min{t; t^2 - n + 1}, where t=floor[sqrt(n-1)]+1.
EXAMPLE
The start of the sequence as triangle array T(n,k) read by rows, row number k contains 2k-1 numbers:
1;
2,2,1;
1,2,3,3,3;
4,4,4,4,3,2,1;
...
If k is odd the row is 1,2,...,k,k...k (k times repetition "k" at the end of row).
If k is even the row is k,k,...k,k-1,k-2,...1 (k times repetition "k" at the start of row).
MATHEMATICA
row[n_] := If[OddQ[n], Range[n-1]~Join~Table[n, {n}], Table[n, {n}]~Join~ Range[n-1, 1, -1]];
row /@ Range[10] // Flatten (* Jean-François Alcover, Nov 19 2019 *)
PROG
(Python)
t=int(math.sqrt(n-1))+1
i=(t % 2)*min(t, n-(t-1)**2) + ((t+1) % 2)*min(t, t**2-n+1)
CROSSREFS
Cf. A081344.
Sequence in context: A242357 A120423 A113137 * A238404 A331910 A240168
KEYWORD
nonn,tabf
AUTHOR
Boris Putievskiy, Dec 16 2012
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)