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

1,2

Comments

Antidiagonal sums = A006578. - Reinhard Zumkeller, Nov 17 2011

Links

Peter Kagey, Antidiagonals n = 1..126 of triangle, flattened

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)

Example

Table begins
  1, 2, 3, 4, 5, ...
  2, 2, 3, 4, 5, ...
  3, 3, 3, 4, 5, ...
  4, 4, 4, 4, 5, ...
  ...

Maple

seq(seq(max(r, d+1-r), r=1..d), d=1..15); # Robert Israel, Jul 22 2016

Mathematica

Flatten[Table[Max[n-k+1, k], {n, 13}, {k, n, 1, -1}]] (* Alonso del Arte, Nov 17 2011 *)

Prog

(PARI) T(n, k) = max(n, k) \\ Charles R Greathouse IV, Feb 07 2017
(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

Crossrefs

Cf. A003056, A003983, A003984, A004197.

Equals A003984(n) + 1.

Sequence in context: A071647 A034883 A338643 * A321126 A342765 A244580

Adjacent sequences: A051122 A051123 A051124 * A051126 A051127 A051128

Keyword

nonn,tabl,easy,nice

Author

N. J. A. Sloane

Extensions

More terms from Robert Lozyniak

Status

approved