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A098353
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Multiplication table of the odd numbers read by antidiagonals.
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3
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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
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history;
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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FORMULA
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EXAMPLE
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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 ...
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MAPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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AUTHOR
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Douglas Stones (dssto1(AT)student.monash.edu.au), Sep 04 2004
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STATUS
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approved
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