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A238013
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List n copies of each k in {1,2,...,n}, for n=1,2,3,...
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7
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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
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1,4
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COMMENTS
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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 n-th 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 k-th row of given length; see Example.
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LINKS
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FORMULA
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EXAMPLE
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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.
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MAPLE
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PROG
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(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 n-th term.
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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