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.

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

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. Adams-Watters, 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(t-1)(2t-1)/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 n-th term. - M. F. Hasler, Feb 17 2014

Crossrefs

Cf. A002260, A002262, A002024.

Cf. A074279, A121997, A238013, A237451, A237452.

Sequence in context: A053824 A033925 A358012 * 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