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A051125 Table T(n,k) = max{n,k} read by antidiagonals (n >= 1, k >= 1).

%I A051125 #42 Feb 17 2022 01:14:57
%S A051125 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,
%T A051125 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,
%U A051125 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
%N A051125 Table T(n,k) = max{n,k} read by antidiagonals (n >= 1, k >= 1).
%C A051125 Antidiagonal sums = A006578. - _Reinhard Zumkeller_, Nov 17 2011
%H A051125 Peter Kagey, <a href="/A051125/b051125.txt">Antidiagonals n = 1..126 of triangle, flattened</a>
%F A051125 From _Robert Israel_, Jul 22 2016: (Start)
%F A051125 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).
%F A051125 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)
%e A051125 Table begins
%e A051125   1, 2, 3, 4, 5, ...
%e A051125   2, 2, 3, 4, 5, ...
%e A051125   3, 3, 3, 4, 5, ...
%e A051125   4, 4, 4, 4, 5, ...
%e A051125   ...
%p A051125 seq(seq(max(r,d+1-r),r=1..d),d=1..15); # _Robert Israel_, Jul 22 2016
%t A051125 Flatten[Table[Max[n-k+1, k], {n, 13}, {k, n, 1, -1}]] (* _Alonso del Arte_, Nov 17 2011 *)
%o A051125 (PARI) T(n,k) = max(n,k) \\ _Charles R Greathouse IV_, Feb 07 2017
%o A051125 (Magma) [Max(n-k+1,k): k in [1..n], n in [1..15]]; // _G. C. Greubel_, Jul 23 2019
%o A051125 (Sage) [[max(n-k+1,k) for k in (1..n)] for n in (1..15)] # _G. C. Greubel_, Jul 23 2019
%o A051125 (GAP) Flat(List([1..15], n-> List([1..n], k-> Maximum(n-k+1,k) ))); # _G. C. Greubel_, Jul 23 2019
%Y A051125 Cf. A003056, A003983, A003984, A004197.
%Y A051125 Equals A003984(n) + 1.
%K A051125 nonn,tabl,easy,nice
%O A051125 1,2
%A A051125 _N. J. A. Sloane_
%E A051125 More terms from Robert Lozyniak