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A051125 Table T(n,k) = max{n,k} read by antidiagonals (n >= 1, k >= 1). 10
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)
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

CROSSREFS

Cf. A003984, A003983, A004197, A003056.

A003984(n) + 1

Sequence in context: A070081 A034883 A071647 * A244580 A131830 A147952

Adjacent sequences:  A051122 A051123 A051124 * A051126 A051127 A051128

KEYWORD

nonn,tabl,easy,nice,changed

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Robert Lozyniak

STATUS

approved

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Last modified June 27 11:25 EDT 2017. Contains 288788 sequences.