A285192 Array read by antidiagonals: T(n,k) = n*k*(3+n*k)/2 (n >= 0, k >= 0).

0, 0, 0, 0, 2, 0, 0, 5, 5, 0, 0, 9, 14, 9, 0, 0, 14, 27, 27, 14, 0, 0, 20, 44, 54, 44, 20, 0, 0, 27, 65, 90, 90, 65, 27, 0, 0, 35, 90, 135, 152, 135, 90, 35, 0, 0, 44, 119, 189, 230, 230, 189, 119, 44, 0, 0, 54, 152, 252, 324, 350, 324, 252, 152, 54, 0

Offset

0,5

Links

Robert Israel, Table of n, a(n) for n = 0..10152

Formula

G.f. as array: xy (2-x-y+2xy)/((1-x)^3 (1-y)^3). - Robert Israel, Apr 26 2017

Example

Array begins:
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...]
[0, 2, 5, 9, 14, 20, 27, 35, 44, 54, ...]
[0, 5, 14, 27, 44, 65, 90, 119, 152, 189, ...]
[0, 9, 27, 54, 90, 135, 189, 252, 324, 405, ...]
[0, 14, 44, 90, 152, 230, 324, 434, 560, 702, ...]
[0, 20, 65, 135, 230, 350, 495, 665, 860, 1080, ...]
[0, 27, 90, 189, 324, 495, 702, 945, 1224, 1539, ...]
...

Maple

T:= (n, k) -> n*k*(3+n*k)/2:
seq(seq(T(k, n-k), k=0..n), n=0..10); # Robert Israel, Apr 26 2017

Mathematica

Table[# k (3 + # k)/2 &[n - k], {n, 0, 10}, {k, n, 0, -1}] // Flatten (* Michael De Vlieger, Apr 26 2017 *)

Crossrefs

Row 1 is A000096, row 2 is A014106, etc.

Sequence in context: A361521 A223705 A358304 * A278177 A095221 A078112

Adjacent sequences: A285189 A285190 A285191 * A285193 A285194 A285195

Keyword

nonn,tabl,easy

Author

N. J. A. Sloane, Apr 26 2017, based on an email message from Andras W. Ferencz.

Status

approved