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A051125
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Table T(n,k) = max{n,k} read by antidiagonals (n >= 1, k >= 1).
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15
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1, 2, 2, 3, 2, 3, 4, 3, 3, 4, 5, 4, 3, 4, 5, 6, 5, 4, 4, 5, 6, 7, 6, 5, 4, 5, 6, 7, 8, 7, 6, 5, 5, 6, 7, 8, 9, 8, 7, 6, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 7, 8, 9, 10, 11, 12, 11, 10, 9, 8, 7, 7, 8, 9, 10, 11, 12, 13, 12, 11, 10, 9, 8, 7, 8, 9, 10, 11, 12, 13, 14, 13
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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G.f. as table: G(x,y) = x*y*(1-3*x*y+x*y^2+x^2*y)/((1-x*y)*(1-x)^2*(1-y)^2).
G.f. flattened: (1-x)^(-2)*(x^2 + Sum_{j >= 0} x^(2*j^2) *(x+x^2 -2*x^(j+2)-2*x^(-j+2)+2*x^(2*j+2))). (End)
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EXAMPLE
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Table begins
1, 2, 3, 4, 5, ...
2, 2, 3, 4, 5, ...
3, 3, 3, 4, 5, ...
4, 4, 4, 4, 5, ...
...
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MAPLE
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seq(seq(max(r, d+1-r), r=1..d), d=1..15); # Robert Israel, Jul 22 2016
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MATHEMATICA
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Flatten[Table[Max[n-k+1, k], {n, 13}, {k, n, 1, -1}]] (* Alonso del Arte, Nov 17 2011 *)
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PROG
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(Magma) [Max(n-k+1, k): k in [1..n], n in [1..15]]; // G. C. Greubel, Jul 23 2019
(Sage) [[max(n-k+1, k) for k in (1..n)] for n in (1..15)] # G. C. Greubel, Jul 23 2019
(GAP) Flat(List([1..15], n-> List([1..n], k-> Maximum(n-k+1, k) ))); # G. C. Greubel, Jul 23 2019
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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More terms from Robert Lozyniak
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STATUS
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approved
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