

A227089


T(n,k)=Number of nXk binary arrays indicating whether each 2X2 subblock of a larger binary array has lexicographically increasing rows and columns, for some larger (n+1)X(k+1) binary array with rows and columns of the latter in lexicographically nondecreasing order


6



2, 4, 4, 7, 12, 7, 11, 29, 29, 11, 16, 62, 99, 62, 16, 22, 122, 302, 302, 122, 22, 29, 225, 842, 1339, 842, 225, 29, 37, 393, 2177, 5517, 5517, 2177, 393, 37, 46, 655, 5281, 21335, 34862, 21335, 5281, 655, 46, 56, 1048, 12128, 77706, 210279, 210279, 77706, 12128
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OFFSET

1,1


COMMENTS

Table starts
..2....4.....7.....11.......16.........22..........29............37
..4...12....29.....62......122........225.........393...........655
..7...29....99....302......842.......2177........5281.........12128
.11...62...302...1339.....5517......21335.......77706........267130
.16..122...842...5517....34862.....210279.....1198995.......6435794
.22..225..2177..21335...210279....2016091....18423194.....158636376
.29..393..5281..77706..1198995...18423194...272856711....3820696108
.37..655.12128.267130..6435794..158636376..3820696108...87559140736
.46.1048.26548.868999.32506602.1281809749.50204897327.1887451154541


LINKS

R. H. Hardin, Table of n, a(n) for n = 1..144


FORMULA

Empirical for column k:
k=1: a(n) = (1/2)*n^2 + (1/2)*n + 1
k=2: a(n) = (1/120)*n^5 + (1/24)*n^4 + (5/24)*n^3 + (35/24)*n^2 + (77/60)*n + 1
k=3: [polynomial of degree 11]
k=4: [polynomial of degree 23]
k=5: [polynomial of degree 47] for n>3


EXAMPLE

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


CROSSREFS

Column 1 is A000124
Sequence in context: A297607 A223770 A223777 * A225900 A227558 A296651
Adjacent sequences: A227086 A227087 A227088 * A227090 A227091 A227092


KEYWORD

nonn,tabl


AUTHOR

R. H. Hardin Jun 30 2013


STATUS

approved



