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%I #12 Mar 17 2018 16:46:52
%S 1,1,2,1,1,2,2,1,1,2,2,4,1,1,2,2,4,4,1,1,2,2,4,4,8,1,1,2,2,4,4,8,8,1,
%T 1,2,2,4,4,8,8,16,1,1,2,2,4,4,8,8,16,16,1,1,2,2,4,4,8,8,16,16,32,1,1,
%U 2,2,4,4,8,8,16,16,32,32,1,1,2,2,4,4,8,8,16,16,32,32,64
%N Triangle giving maximal permanent P(n,k) of an n X n lower Hessenberg (0,1)-matrix with exactly k 1's for 2 <= n <= k <= 2n, read by rows.
%H G. C. Greubel, <a href="/A113453/b113453.txt">Table of n, a(n) for rows 2 to 50, flattened</a>
%H D. D. Olesky, B. L. Shader and P. van den Driessche, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v12i1r70/0">Permanents of Hessenberg (0,1)-matrices</a>, Electronic Journal of Combinatorics, 12 (2005) #R70.
%H B. Shader <a href="http://www.uwyo.edu/bshader/hesstable.pdf">Table of known values of P(n,k) for n<=12.</a>
%F P(n, k) = 2^(floor((k-n)/2)), if n <= k <= 2n.
%t Table[2^(Floor[(k - n)/2]), {n, 2, 51}, {k, n, 2*n}] // Flatten (* _G. C. Greubel_, Mar 11 2017 *)
%o (PARI) for(n=2,25, for(k=n,2*n, print1(2^(floor((k-n)/2)), ", "))) \\ _G. C. Greubel_, Mar 11 2017
%Y Cf. A034856, A113452, A113453, A113454, A113455.
%K easy,nonn,tabf
%O 0,3
%A Bryan Shader (bshader(AT)uwyo.edu), Jan 07 2006
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