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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 (list; table; graph; refs; listen; history; text; internal format)
 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 G. C. Greubel, Antidiagonals n = 1..100 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 Cf. A003991, A098352, A204022, A157454. Sequence in context: A213678 A293676 A303714 * A073060 A183526 A337562 Adjacent sequences: A098350 A098351 A098352 * A098354 A098355 A098356 KEYWORD nonn,tabl AUTHOR Douglas Stones (dssto1(AT)student.monash.edu.au), Sep 04 2004 STATUS approved

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Last modified October 3 17:52 EDT 2023. Contains 365870 sequences. (Running on oeis4.)