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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

%I

%S 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,

%T 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,

%U 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

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

%C 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

%C Subsequences start at indices A000330 + 1. - _Ralf Stephan_, Dec 17 2013

%C When sequence fills a triangular array by rows, the main diagonal is A064865:

%C This triangle begins:

%C ....1

%C ...1.2

%C ..3.4.1

%C .2.3.4.5

%C 6.7.8.9.1

%C From _Antti Karttunen_, Feb 17 2014: (Start)

%C A more natural way of organizing this sequence is as an irregular table consisting of successively larger square matrices:

%C 1;

%C 1, 2;

%C 3, 4;

%C 1, 2, 3;

%C 4, 5, 6;

%C 7, 8, 9;

%C 1, 2, 3, 4;

%C 5, 6, 7, 8;

%C 9,10,11,12;

%C 13,14,15,16;

%C etc.

%C (End)

%F a(n) = A237451(n) + (A237452(n)*A074279(n)) + 1. - _M. F. Hasler_, Feb 17 2014

%F 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

%o (PARI) A064866_vec(N=9)=concat(vector(N, i, vector(i^2, j, j))) \\ NB: This creates a vector; use A064866_vec()[n] to get the n-th term. - _M. F. Hasler_, Feb 17 2014

%Y Cf. A002260, A002262, A002024.

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

%K easy,nonn,tabl

%O 1,3

%A _Floor van Lamoen_, Oct 08 2001

%E Edited by _Ralf Stephan_, Dec 17 2013

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Last modified December 4 11:13 EST 2016. Contains 278750 sequences.