cp's OEIS Frontend

A098353 Multiplication table of the odd numbers read by antidiagonals.

%I A098353 #22 Sep 08 2022 08:45:15
%S A098353 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 A098353 33,13,15,39,55,63,63,55,39,15,17,45,65,77,81,77,65,45,17,19,51,75,91,
%U A098353 99,99,91,75,51,19,21,57,85,105,117,121,117,105,85,57,21
%N A098353 Multiplication table of the odd numbers read by antidiagonals.
%C A098353 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 A098353 G. C. Greubel, <a href="/A098353/b098353.txt">Antidiagonals n = 1..100</a>
%F A098353 a(n) = A204022(n,k) * A157454(n,k). - _Ridouane Oudra_, Jul 20 2019
%e A098353 Array begins:
%e A098353    1,  3,  5,  7,  9,  11 ...
%e A098353    3,  9, 15, 21, 27,  33 ...
%e A098353    5, 15, 25, 35, 45,  55 ...
%e A098353    7, 21, 35, 49, 63,  77 ...
%e A098353    9, 27, 45, 63, 81,  99 ...
%e A098353   11, 33, 55, 77, 99, 121 ...
%p A098353 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 A098353 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 A098353 (PARI) {T(n, k) = max(2*k-1, 2*(n-k)+1)*min(2*k-1, 2*(n-k)+1)};
%o A098353 for(n=1, 12, for(k=1, n, print1(T(n, k), ", "))) \\ _G. C. Greubel_, Jul 23 2019
%o A098353 (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 A098353 (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 A098353 (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 A098353 Cf. A003991, A098352, A204022, A157454.
%K A098353 nonn,tabl
%O A098353 1,2
%A A098353 Douglas Stones (dssto1(AT)student.monash.edu.au), Sep 04 2004