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A242549 T(n,k)=Number of length n+3 0..k arrays with no four elements in a row with pattern aabb (possibly a=b) and new values 0..k introduced in 0..k order 8

%I #4 May 17 2014 09:37:52

%S 6,12,9,13,32,15,13,42,88,25,13,43,150,242,40,13,43,165,554,660,64,13,

%T 43,166,690,2072,1800,104,13,43,166,711,3050,7808,4920,169,13,43,166,

%U 712,3311,13988,29536,13448,273,13,43,166,712,3339,16512,65588,111878,36736

%N T(n,k)=Number of length n+3 0..k arrays with no four elements in a row with pattern aabb (possibly a=b) and new values 0..k introduced in 0..k order

%C Table starts

%C ...6.....12......13......13.......13.......13.......13.......13.......13

%C ...9.....32......42......43.......43.......43.......43.......43.......43

%C ..15.....88.....150.....165......166......166......166......166......166

%C ..25....242.....554.....690......711......712......712......712......712

%C ..40....660....2072....3050.....3311.....3339.....3340.....3340.....3340

%C ..64...1800....7808...13988....16512....16968....17004....17005....17005

%C .104...4920...29536...65588....86671....92360....93103....93148....93149

%C .169..13448..111878..311431...471698...532175...543773...544920...544975

%C .273..36736..423969.1489435..2631790..3210136..3362689..3384566..3386262

%C .441.100352.1607058.7152787.14930915.20066475.21854355.22202698.22241481

%H R. H. Hardin, <a href="/A242549/b242549.txt">Table of n, a(n) for n = 1..9999</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1) +a(n-3) +a(n-4)

%F k=2: a(n) = 2*a(n-1) +4*a(n-3) +4*a(n-4)

%F k=3: [order 8]

%F k=4: [order 12]

%F k=5: [order 16]

%F k=6: [order 20]

%F k=7: [order 24]

%e Some solutions for n=4 k=4

%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

%e ..1....1....0....0....1....1....1....1....0....1....1....0....1....1....1....0

%e ..2....2....1....1....2....1....1....0....1....2....2....1....2....0....0....1

%e ..1....1....2....0....0....1....2....2....2....3....1....2....3....0....1....2

%e ..0....3....0....2....2....2....1....1....1....4....3....3....0....2....1....3

%e ..1....2....0....3....2....0....1....2....1....4....3....3....0....1....0....1

%e ..2....0....0....1....2....0....3....0....1....4....1....0....0....3....2....2

%Y Column 1 is A006498(n+4)

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, May 17 2014

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Last modified February 29 11:59 EST 2024. Contains 370425 sequences. (Running on oeis4.)