A208142 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 0 1 vertically.

2, 4, 4, 6, 16, 6, 9, 36, 36, 8, 12, 81, 108, 64, 10, 16, 144, 324, 240, 100, 12, 20, 256, 720, 900, 450, 144, 14, 25, 400, 1600, 2400, 2025, 756, 196, 16, 30, 625, 3000, 6400, 6300, 3969, 1176, 256, 18, 36, 900, 5625, 14000, 19600, 14112, 7056, 1728, 324, 20, 42, 1296

Offset: 1

Author

R. H. Hardin Feb 23 2012

Keywords

• nonn
• tabl

Comments

Table starts

..2...4....6.....9....12.....16.....20......25......30.......36.......42

..4..16...36....81...144....256....400.....625.....900.....1296.....1764

..6..36..108...324...720...1600...3000....5625....9450....15876....24696

..8..64..240...900..2400...6400..14000...30625...58800...112896...197568

.10.100..450..2025..6300..19600..49000..122500..264600...571536..1111320

.12.144..756..3969.14112..50176.141120..396900..952560..2286144..4889808

.14.196.1176..7056.28224.112896.352800.1102500.2910600..7683984.17929296

.16.256.1728.11664.51840.230400.792000.2722500.7840800.22581504.57081024

Examples

			Some solutions for n=4 k=3
..1..0..0....0..0..0....0..1..0....1..1..1....0..1..0....0..1..0....0..1..0
..0..0..0....1..0..0....1..1..0....1..1..0....1..0..0....0..1..0....1..0..1
..0..0..0....0..0..0....1..1..0....1..0..0....1..0..0....0..1..0....0..0..0
..0..0..0....0..0..0....1..0..0....1..0..0....1..0..0....0..1..0....0..0..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..4508

Crossrefs

Column 1 is A004275(n+1)

Column 2 is A016742

Column 3 is A202195(n-2)

Row 1 is A002620(n+2)

Row 2 is A030179(n+2)

Row 3 is A202093(n-2)

Formula

Empirical for column k:

k=1: a(n) = 2*n

k=2: a(n) = 4*n^2

k=3: a(n) = 3*n^3 + 3*n^2

k=4: a(n) = (9/4)*n^4 + (9/2)*n^3 + (9/4)*n^2

k=5: a(n) = n^5 + 4*n^4 + 5*n^3 + 2*n^2

k=6: a(n) = (4/9)*n^6 + (8/3)*n^5 + (52/9)*n^4 + (16/3)*n^3 + (16/9)*n^2

k=7: a(n) = (5/36)*n^7 + (5/4)*n^6 + (155/36)*n^5 + (85/12)*n^4 + (50/9)*n^3 + (5/3)*n^2