OFFSET
1,2
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
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
KEYWORD
nonn,tabf
AUTHOR
Boris Putievskiy, Dec 16 2012
STATUS
approved