A113453 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.

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, 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, 2, 2, 4, 4, 8, 8, 16, 16, 32, 32, 1, 1, 2, 2, 4, 4, 8, 8, 16, 16, 32, 32, 64

Offset: 0

Author

Bryan Shader (bshader(AT)uwyo.edu), Jan 07 2006

Keywords

• easy
• nonn
• tabf

Links

• G. C. Greubel, Table of n, a(n) for rows 2 to 50, flattened
• D. D. Olesky, B. L. Shader and P. van den Driessche, Permanents of Hessenberg (0,1)-matrices, Electronic Journal of Combinatorics, 12 (2005) #R70.
• B. Shader Table of known values of P(n,k) for n<=12.

Crossrefs

Cf. A034856, A113452, A113453, A113454, A113455.

Programs

Mathematica

Table[2^(Floor[(k - n)/2]), {n, 2, 51}, {k, n, 2*n}] // Flatten (* G. C. Greubel, Mar 11 2017 *)

PARI

for(n=2,25, for(k=n,2*n, print1(2^(floor((k-n)/2)), ", "))) \\ G. C. Greubel, Mar 11 2017

Formula

P(n, k) = 2^(floor((k-n)/2)), if n <= k <= 2n.