

A238013


List n copies of each k in {1,2,...,n}, for n=1,2,3,...


7



1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 2, 3, 3, 3, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5
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OFFSET

1,4


COMMENTS

Consider a sequence of matrices of size 1 X 1, 2 X 2, 3 X 3, etc., then list their elements, read by rows. The present sequence gives the row index of the nth term of the sequence within "its" matrix, numbered by A074279(n); the column index being given by A121997.
The sequence could be seen as irregular table or triangle with row lengths equal to 1,2,2,3,3,3,4,4,4,4,... = A002024, each row being filled with k's, for the kth row of given length; see Example.


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = A237452(n)+1.  Antti Karttunen, Feb 17 2014


EXAMPLE

Formatted as table with row lengths given by A002024 = 1, 2,2, 3,3,3, ... the sequence reads:
1 \\ 1 copy of "1";
1 1 \\ 2 copies of "1", then
2 2 \\ 2 copies of "2";
1 1 1 \\ 3 copies of "1", then
2 2 2 \\ 3 copies of "2", etc.
3 3 3 \\
1 1 1 1 \\ 1st row of length 4 => filled with "1"s
2 2 2 2 \\ 2nd row of length 4 => filled with "2"s
3 3 3 3 \\ 3rd row of length 4 => filled with "3"s
4 4 4 4 \\ etc.


MAPLE

seq(seq(i$j, i=1..j), j=1..10); # Robert Israel, May 29 2017


PROG

(PARI) for(i=1, 9, for(j=1, i, for(k=1, i, print1(j", "))))
(PARI) A238013_vec(N=9)=concat(vector(N, i, concat(vector(i, j, vector(i, k, i))))) \\ Note: this creates a vector; use A238013_vec()[n] to get the nth term.


CROSSREFS

Cf. A121997, A237451, A237452, A002024, A074279.
Sequence in context: A105224 A261627 A237112 * A303940 A280134 A143488
Adjacent sequences: A238010 A238011 A238012 * A238014 A238015 A238016


KEYWORD

nonn,tabf


AUTHOR

M. F. Hasler, Feb 16 2014


STATUS

approved



