A051125 Table T(n,k) = max{n,k} read by antidiagonals (n >= 1, k >= 1).
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
Offset: 1
Examples
Table begins 1, 2, 3, 4, 5, ... 2, 2, 3, 4, 5, ... 3, 3, 3, 4, 5, ... 4, 4, 4, 4, 5, ... ...
Links
- Peter Kagey, Antidiagonals n = 1..126 of triangle, flattened
Programs
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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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Magma
[Max(n-k+1,k): k in [1..n], n in [1..15]]; // G. C. Greubel, Jul 23 2019
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Maple
seq(seq(max(r,d+1-r),r=1..d),d=1..15); # Robert Israel, Jul 22 2016
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Mathematica
Flatten[Table[Max[n-k+1, k], {n, 13}, {k, n, 1, -1}]] (* Alonso del Arte, Nov 17 2011 *) -
PARI
T(n,k) = max(n,k) \\ Charles R Greathouse IV, Feb 07 2017
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Sage
[[max(n-k+1,k) for k in (1..n)] for n in (1..15)] # G. C. Greubel, Jul 23 2019
Formula
From Robert Israel, Jul 22 2016: (Start)
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)
Extensions
More terms from Robert Lozyniak
Comments