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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 (list; table; graph; refs; listen; history; text; internal format)
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: 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

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Last modified March 2 09:45 EST 2021. Contains 341746 sequences. (Running on oeis4.)