

A064866


Write numbers 1, then 1 up to 2^2, then 1 up to 3^2, then 1 up to 4^2 and so on.


6



1, 1, 2, 3, 4, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28
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OFFSET

1,3


COMMENTS

This is a fractal sequence: if the first instance of each number is deleted, the original sequence is recovered.  Franklin T. AdamsWatters, Dec 14 2013
Subsequences start at indices A000330 + 1.  Ralf Stephan, Dec 17 2013
When sequence fills a triangular array by rows, the main diagonal is A064865:
This triangle begins:
....1
...1.2
..3.4.1
.2.3.4.5
6.7.8.9.1
From Antti Karttunen, Feb 17 2014: (Start)
A more natural way of organizing this sequence is as an irregular table consisting of successively larger square matrices:
1;
1, 2;
3, 4;
1, 2, 3;
4, 5, 6;
7, 8, 9;
1, 2, 3, 4;
5, 6, 7, 8;
9,10,11,12;
13,14,15,16;
etc.
(End)


LINKS

Table of n, a(n) for n=1..83.


FORMULA

a(n) = A237451(n) + (A237452(n)*A074279(n)) + 1.  M. F. Hasler, Feb 17 2014
For 1 <= n <= 650, a(n) = n  t(t1)(2t1)/6, where t = floor((3*n)^(1/3)+1/2).  Mikael Aaltonen, Jan 17 2015


MATHEMATICA

Table[Range[n^2], {n, 10}]//Flatten (* Harvey P. Dale, Mar 05 2018 *)


PROG

(PARI) A064866_vec(N=9)=concat(vector(N, i, vector(i^2, j, j))) \\ Note: This creates a vector; use A064866_vec()[n] to get the nth term.  M. F. Hasler, Feb 17 2014


CROSSREFS

Cf. A002260, A002262, A002024.
Cf. A074279, A121997, A238013, A237451, A237452.
Sequence in context: A283365 A053824 A033925 * A024855 A274651 A074057
Adjacent sequences: A064863 A064864 A064865 * A064867 A064868 A064869


KEYWORD

easy,nonn,tabl


AUTHOR

Floor van Lamoen, Oct 08 2001


EXTENSIONS

Edited by Ralf Stephan, Dec 17 2013


STATUS

approved



