A327273 - OEIS

%I #11 Nov 28 2019 07:54:11

%S 1,5,105,425,144925,580125,243697125,46420625,253459513125

%N An upper bound sequence for A327272.

%C a(n) can be calculated by a faster algorithm than that for A327272(n). It gives a small (but not necessarily smallest) positive determinant with top row [1,2,2^2,...,2^n] and all entries integers, and rows orthogonal. Note that a(n) = A327272(n) for n=0,1 and 3. See Pinner and Smyth link below for both algorithms, and more details of the sequences.

%H Chris Pinner and Chris Smyth, <a href="https://www.maths.ed.ac.uk/~chris/papers/MinimalLattices040919.pdf">Lattices of minimal index in Z^n having an orthogonal basis containing a given basis vector</a>

%H Christopher J. Smyth, <a href="/A327273/a327273.pdf">List of n, a(n) and associated matrix for 0 <= n <= 8</a>

%e a(2) = 105 since the algorithm for a(n) produces the determinant([[1,2,4],[2,-1,0],[4,8,-5]]) = 105, having top row [1,2,2^2] and all rows orthogonal.

%K nonn,more

%O 0,2

%A _Christopher J. Smyth_, Sep 09 2019