A202052 T(n,k)=Number of (n+2)X(k+2) binary arrays avoiding patterns 001 and 110 in rows and columns.

102, 216, 216, 390, 528, 390, 636, 1080, 1080, 636, 966, 1968, 2470, 1968, 966, 1392, 3304, 4980, 4980, 3304, 1392, 1926, 5216, 9170, 11016, 9170, 5216, 1926, 2580, 7848, 15760, 22092, 22092, 15760, 7848, 2580, 3366, 11360, 25650, 41088, 47950, 41088

Offset: 1

Author

R. H. Hardin Dec 10 2011

Keywords

• nonn
• tabl

Comments

Table starts

..102...216...390....636....966....1392....1926.....2580.....3366.....4296

..216...528..1080...1968...3304....5216....7848....11360....15928....21744

..390..1080..2470...4980...9170...15760...25650....39940....59950....87240

..636..1968..4980..11016..22092...41088...71964...120000...192060...296880

..966..3304..9170..22092..47950...95984..180054...320180...544390...890904

.1392..5216.15760..41088..95984..205792..411696...777760..1400080..2418432

.1926..7848.25650..71964.180054..411696..874998..1750140..3325410..6046344

.2580.11360.39940.120000.320180..777760.1750140..3694920..7390020.14108400

.3366.15928.59950.192060.544390.1400080.3325410..7390020.15519262.31038744

.4296.21744.87240.296880.890904.2418432.6046344.14108400.31038744.64899456

Examples

			Some solutions for n=5 k=3
..0..0..0..0..0....1..0..1..1..1....0..1..0..1..1....0..1..0..1..1
..1..1..1..1..1....0..1..0..0..0....1..0..1..0..0....1..0..0..0..0
..0..0..0..0..0....1..0..1..1..1....0..1..0..1..0....0..1..0..1..1
..0..1..1..1..1....0..0..0..0..0....0..0..0..0..0....1..0..0..0..0
..0..1..0..0..0....1..0..1..1..1....0..1..0..1..0....0..1..0..1..1
..0..1..0..1..1....0..0..0..0..0....0..1..0..1..0....0..0..0..0..0
..0..1..0..1..0....1..0..1..0..0....0..1..0..1..0....0..1..0..1..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..511

Crossrefs

Column 1 is A086113(n+2)

Column 2 is A086114(n+2)

Column 3 is A086115(n+2)

Diagonal is A032260(n+2)

Formula

Empirical (via A086113): T(n,k)=2*(n+2)*(2*binomial(n+k+3,n+2)-k-2)

Empirical for columns:

T(n,1) = 2*n^3 + 18*n^2 + 46*n + 36

T(n,2) = (2/3)*n^4 + (28/3)*n^3 + (142/3)*n^2 + (284/3)*n + 64

T(n,3) = (1/6)*n^5 + (10/3)*n^4 + (155/6)*n^3 + (290/3)*n^2 + 164*n + 100

T(n,4) = (1/30)*n^6 + (9/10)*n^5 + (59/6)*n^4 + (111/2)*n^3 + (2552/15)*n^2 + (1278/5)*n + 144

T(n,5) = (1/180)*n^7 + (7/36)*n^6 + (511/180)*n^5 + (805/36)*n^4 + (4606/45)*n^3 + (2443/9)*n^2 + (1854/5)*n + 196

T(n,6) = (1/1260)*n^8 + (11/315)*n^7 + (59/90)*n^6 + (308/45)*n^5 + (7807/180)*n^4 + (7667/45)*n^3 + (14139/35)*n^2 + (17876/35)*n + 256

T(n,7) = (1/10080)*n^9 + (3/560)*n^8 + (211/1680)*n^7 + (67/40)*n^6 + (6709/480)*n^5 + (6041/80)*n^4 + (663941/2520)*n^3 + (79913/140)*n^2 + (4735/7)*n + 324