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A202052 T(n,k)=Number of (n+2)X(k+2) binary arrays avoiding patterns 001 and 110 in rows and columns 5
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,1
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
LINKS
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
EXAMPLE
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
CROSSREFS
Column 1 is A086113(n+2)
Column 2 is A086114(n+2)
Column 3 is A086115(n+2)
Diagonal is A032260(n+2)
Sequence in context: A197816 A078787 A160850 * A284450 A173968 A173969
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Dec 10 2011
STATUS
approved

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Last modified June 15 13:08 EDT 2024. Contains 373407 sequences. (Running on oeis4.)