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Search: id:A003983
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| A003983 |
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Array read by antidiagonals with T(n,k) = min(n,k). |
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+0
21
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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
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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Also, "correlation triangle" for the constant sequence 1. - Paul Barry (pbarry(AT)wit.ie), Jan 16 2006
Antidiagonal sums are in A002620.
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 (pbarry(AT)wit.ie), Jan 16 2006
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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 (pbarry(AT)wit.ie), Jan 16 2006
G.f.: 1/((1-x)*(1-x*y)*(1-x^2*y)) (Christian G. Bower (bowerc(AT)usa.net), Jan 17 2006)
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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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CROSSREFS
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Cf. A002620, A001399, A087062, A115236, A115237, A124258.
Sequence in context: A156593 A054526 A113453 this_sequence A087062 A110537 A144434
Adjacent sequences: A003980 A003981 A003982 this_sequence A003984 A003985 A003986
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KEYWORD
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tabl,nonn,easy,nice
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AUTHOR
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Marc LeBrun (mlb(AT)well.com)
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Nov 08 2000
Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Dec 05 2006
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