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A098359 Multiplication table of the square numbers read by antidiagonals.

%I A098359 #17 May 19 2025 15:35:01
%S A098359 1,4,4,9,16,9,16,36,36,16,25,64,81,64,25,36,100,144,144,100,36,49,144,
%T A098359 225,256,225,144,49,64,196,324,400,400,324,196,64,81,256,441,576,625,
%U A098359 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
%N A098359 Multiplication table of the square numbers read by antidiagonals.
%C A098359 sum_{k=0..2n-2} (-1)^k*a(A000124(2n-2)+k-1) = n. See A003991. - _Charlie Marion_, Apr 22 2013
%F A098359 A(n,k) = n^2*k^2.
%F A098359 G.f.: [xy(1+x)(1+y)] / [(1-x)^3 * (1-y)^3 ]. - _Ralf Stephan_, Oct 27 2004
%F A098359 Sum_{j=1..n} A(j,1+n-j)*j = A213547(n). - _Alois P. Heinz_, May 19 2025
%e A098359 Square array A(n,k) begins:
%e A098359    1,   4,   9,  16,   25,   36,   49, ...
%e A098359    4,  16,  36,  64,  100,  144,  196, ...
%e A098359    9,  36,  81, 144,  225,  324,  441, ...
%e A098359   16,  64, 144, 256,  400,  576,  784, ...
%e A098359   25, 100, 225, 400,  625,  900, 1225, ...
%e A098359   36, 144, 324, 576,  900, 1296, 1764, ...
%e A098359   49, 196, 441, 784, 1225, 1764, 2401, ...
%p A098359 A:= (n,k)-> (n*k)^2:
%p A098359 seq(seq(A(n, 1+d-n), n=1..d), d=1..12);  # _Alois P. Heinz_, May 19 2025
%Y A098359 Cf. A000290, A003991, A098358, A098360, A098361, A213547.
%Y A098359 Antidiagonal sums give A033455.
%Y A098359 Main diagonal gives A000583.
%K A098359 nonn,tabl
%O A098359 1,2
%A A098359 Douglas Stones (dssto1(AT)student.monash.edu.au), Sep 04 2004
%E A098359 Offset corrected by _Alois P. Heinz_, May 19 2025