A098353 Multiplication table of the odd numbers read by antidiagonals.
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
Examples
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 ...
Links
- G. C. Greubel, Antidiagonals n = 1..100
Programs
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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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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
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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
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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 *) -
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 -
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
Comments