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

1,1

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

Links

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

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

Example

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

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)

Sequence in context: A333823 A207254 A207403 * A207024 A207169 A207111

Adjacent sequences: A208139 A208140 A208141 * A208143 A208144 A208145

Keyword

nonn,tabl

Author

R. H. Hardin Feb 23 2012

Status

approved