A113455 Triangle giving maximal permanent P(n,k) of an n X n lower Hessenberg (0,1)-matrix with exactly k 1's for n >= 3 and h(n) - h(floor(n/2)) <= k <= h(n) read by row, where h(n)= (n^2+3n-2)/2 is the sequence A034856.

3, 4, 4, 5, 6, 7, 8, 12, 13, 14, 15, 16, 20, 22, 24, 26, 28, 29, 30, 31, 32, 52, 54, 56, 58, 60, 61, 62, 63, 64, 96, 100, 104, 108, 112, 116, 118, 120, 122, 124, 125, 126, 127, 128, 224, 228, 232, 236, 240, 244, 246, 248, 250, 252, 253, 254, 255, 256, 432, 440, 448

Offset: 0

Author

Bryan Shader (bshader(AT)uwyo.edu), Jan 07 2006; corrected Jan 20 2006

Keywords

• easy
• nonn
• tabf

Links

• 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.

Formula

P(n, k) = s(1) + s(2) + ... + s(k) where s(k) is the sequence A113453.