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A003983
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Array read by antidiagonals with T(n,k) = min(n,k).
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43
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1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 3, 2, 1, 1, 2, 3, 3, 2, 1, 1, 2, 3, 4, 3, 2, 1, 1, 2, 3, 4, 4, 3, 2, 1, 1, 2, 3, 4, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 7, 6, 5, 4, 3, 2, 1
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,5
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COMMENTS
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Also, "correlation triangle" for the constant sequence 1. - Paul Barry, Jan 16 2006
As a triangle, row sums are A002620. T(2n,n)=n+1. Diagonal sums are A001399. Construction: Take antidiagonal triangle of MM^T where M is the sequence array for the constant sequence 1 (lower triangular matrix with all 1's). - Paul Barry, Jan 16 2006
As a triangle, count up to ceiling(n/2) and back down again (repeating the central term when n is even).
When the first two instances of each number are removed from the sequence, the original sequence is recovered.
(End)
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LINKS
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FORMULA
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Number triangle T(n, k) = Sum_{j=0..n} [j<=k][j<=n-k]. - Paul Barry, Jan 16 2006
a(n) = min(floor( 1/2 + sqrt(2*n)) - (2*n + round(sqrt(2*n)) - round(sqrt(2*n))^2)/2+1, (2*n + round(sqrt(2*n)) - round(sqrt(2*n))^2)/2). - Leonid Bedratyuk, Dec 13 2009
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EXAMPLE
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Triangle version begins
1;
1, 1;
1, 2, 1;
1, 2, 2, 1;
1, 2, 3, 2, 1;
1, 2, 3, 3, 2, 1;
1, 2, 3, 4, 3, 2, 1;
1, 2, 3, 4, 4, 3, 2, 1;
1, 2, 3, 4, 5, 4, 3, 2, 1;
...
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MAPLE
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a(n) = min(floor(1/2 + sqrt(2*n)) - (2*n + round(sqrt(2*n)) - round(sqrt(2*n))^2)/2+1, (2*n + round(sqrt(2*n)) - round(sqrt(2*n))^2)/2) # Leonid Bedratyuk, Dec 13 2009
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MATHEMATICA
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PROG
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(Haskell)
a003983 n k = a003983_tabl !! (n-1) !! (k-1)
a003983_tabl = map a003983_row [1..]
a003983_row n = hs ++ drop m (reverse hs)
where hs = [1..n' + m]
(n', m) = divMod n 2
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CROSSREFS
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Cf. A002620, A001399, A087062, A115236, A115237, A124258, A006752, A120268, A173945, A173947, A173948, A173949, A173953, A173954, A173955, A173973, A173982-A173986, A004197.
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KEYWORD
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AUTHOR
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Nov 08 2000
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STATUS
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approved
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