A098359 Multiplication table of the square numbers read by antidiagonals.

1, 4, 4, 9, 16, 9, 16, 36, 36, 16, 25, 64, 81, 64, 25, 36, 100, 144, 144, 100, 36, 49, 144, 225, 256, 225, 144, 49, 64, 196, 324, 400, 400, 324, 196, 64, 81, 256, 441, 576, 625, 576, 441, 256, 81, 100, 324, 576, 784, 900, 900, 784, 576, 324, 100, 121, 400, 729, 1024, 1225, 1296, 1225, 1024, 729, 400, 121

Offset: 1

Author

Douglas Stones (dssto1(AT)student.monash.edu.au), Sep 04 2004

Keywords

• nonn
• tabl

Comments

sum_{k=0..2n-2} (-1)^k*a(A000124(2n-2)+k-1) = n. See A003991. - Charlie Marion, Apr 22 2013

Examples

			Square array A(n,k) begins:
   1,   4,   9,  16,   25,   36,   49, ...
   4,  16,  36,  64,  100,  144,  196, ...
   9,  36,  81, 144,  225,  324,  441, ...
  16,  64, 144, 256,  400,  576,  784, ...
  25, 100, 225, 400,  625,  900, 1225, ...
  36, 144, 324, 576,  900, 1296, 1764, ...
  49, 196, 441, 784, 1225, 1764, 2401, ...
		

Crossrefs

Cf. A000290, A003991, A098358, A098360, A098361, A213547.

Antidiagonal sums give A033455.

Main diagonal gives A000583.

Programs

Maple

A:= (n,k)-> (n*k)^2:
seq(seq(A(n, 1+d-n), n=1..d), d=1..12);  # Alois P. Heinz, May 19 2025

Formula

A(n,k) = n^2*k^2.

G.f.: [xy(1+x)(1+y)] / [(1-x)^3 * (1-y)^3 ]. - Ralf Stephan, Oct 27 2004

Sum_{j=1..n} A(j,1+n-j)*j = A213547(n). - Alois P. Heinz, May 19 2025

Extensions

Offset corrected by Alois P. Heinz, May 19 2025