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A098353
Multiplication table of the odd numbers read by antidiagonals.
3
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, 33, 13, 15, 39, 55, 63, 63, 55, 39, 15, 17, 45, 65, 77, 81, 77, 65, 45, 17, 19, 51, 75, 91, 99, 99, 91, 75, 51, 19, 21, 57, 85, 105, 117, 121, 117, 105, 85, 57, 21
OFFSET
1,2
COMMENTS
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
LINKS
FORMULA
a(n) = A204022(n,k) * A157454(n,k). - Ridouane Oudra, Jul 20 2019
EXAMPLE
Array begins:
1, 3, 5, 7, 9, 11 ...
3, 9, 15, 21, 27, 33 ...
5, 15, 25, 35, 45, 55 ...
7, 21, 35, 49, 63, 77 ...
9, 27, 45, 63, 81, 99 ...
11, 33, 55, 77, 99, 121 ...
MAPLE
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
MATHEMATICA
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 *)
PROG
(PARI) {T(n, k) = max(2*k-1, 2*(n-k)+1)*min(2*k-1, 2*(n-k)+1)};
for(n=1, 12, for(k=1, n, print1(T(n, k), ", "))) \\ G. C. Greubel, Jul 23 2019
(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
(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
(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
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Douglas Stones (dssto1(AT)student.monash.edu.au), Sep 04 2004
STATUS
approved