%I #22 Sep 08 2022 08:45:15

%S 1,3,3,5,9,5,7,15,15,7,9,21,25,21,9,11,27,35,35,27,11,13,33,45,49,45,

%T 33,13,15,39,55,63,63,55,39,15,17,45,65,77,81,77,65,45,17,19,51,75,91,

%U 99,99,91,75,51,19,21,57,85,105,117,121,117,105,85,57,21

%N Multiplication table of the odd numbers read by antidiagonals.

%C a(n) is also the first row of the denominators of the Gram Matrix generated from the normal equations with inner product of the 2D integral with both ranges -1 to 1 over all even 2D polynomials. Subsequent rows and remaining Gram Matrix rows for other 2D polynomials do not currently appear in the OEIS. - _John Spitzer_, Feb 13 2020

%H G. C. Greubel, <a href="/A098353/b098353.txt">Antidiagonals n = 1..100</a>

%F a(n) = A204022(n,k) * A157454(n,k). - _Ridouane Oudra_, Jul 20 2019

%e Array begins:

%e 1, 3, 5, 7, 9, 11 ...

%e 3, 9, 15, 21, 27, 33 ...

%e 5, 15, 25, 35, 45, 55 ...

%e 7, 21, 35, 49, 63, 77 ...

%e 9, 27, 45, 63, 81, 99 ...

%e 11, 33, 55, 77, 99, 121 ...

%p seq(seq(max(2*k-1, 2*(n-k)+1)*min(2*k-1, 2*(n-k)+1), k = 1..n), n = 1..12); # _G. C. Greubel_, Aug 16 2019

%t Table[Max[2*k-1, 2*(n-k)+1]*Min[2*k-1, 2*(n-k)+1], {n,0,12}, {k,0,n} ]//Flatten (* _G. C. Greubel_, Jul 23 2019 *)

%o (PARI) {T(n, k) = max(2*k-1, 2*(n-k)+1)*min(2*k-1, 2*(n-k)+1)};

%o for(n=1, 12, for(k=1, n, print1(T(n, k), ", "))) \\ _G. C. Greubel_, Jul 23 2019

%o (Magma) [[Max(2*k-1, 2*(n-k)+1)*Min(2*k-1, 2*(n-k)+1): k in [1..n]]: n in [1..12]]; // _G. C. Greubel_, Jul 23 2019

%o (Sage) [[max(2*k-1, 2*(n-k)+1)*min(2*k-1, 2*(n-k)+1) for k in (1..n)] for n in (1..12)] # _G. C. Greubel_, Jul 23 2019

%o (GAP) Flat(List([1..12], n-> List([1..n], k-> Maximum(2*k-1, 2*(n-k)+1) *Minimum(2*k-1, 2*(n-k)+1) ))) # _G. C. Greubel_, Jul 23 2019

%Y Cf. A003991, A098352, A204022, A157454.

%K nonn,tabl

%O 1,2

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