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A227125 T(n,k)=Number of nXk 0,1 arrays indicating 2X2 subblocks of some larger (n+1)X(k+1) binary array having a sum of zero, with rows and columns of the latter in lexicographically nondecreasing order 6
2, 3, 3, 4, 7, 4, 5, 13, 13, 5, 6, 23, 33, 23, 6, 7, 40, 81, 81, 40, 7, 8, 68, 202, 295, 202, 68, 8, 9, 112, 492, 1079, 1079, 492, 112, 9, 10, 178, 1143, 3836, 5820, 3836, 1143, 178, 10, 11, 273, 2524, 12954, 30620, 30620, 12954, 2524, 273, 11, 12, 405, 5315, 41334 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

..2...3....4......5.......6........7..........8...........9............10

..3...7...13.....23......40.......68........112.........178...........273

..4..13...33.....81.....202......492.......1143........2524..........5315

..5..23...81....295....1079.....3836......12954.......41334........124956

..6..40..202...1079....5820....30620.....153955......732611.......3296920

..7..68..492...3836...30620...241783....1840054....13289471......90728418

..8.112.1143..12954..153955..1840054...21458929...238464936....2504527178

..9.178.2524..41334..732611.13289471..238464936..4109192774...67076312881

.10.273.5315.124956.3296920.90728418.2504527178.67076312881.1709864974106

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..180

FORMULA

Empirical for column k:

k=1: a(n) = n + 1

k=2: a(n) = (1/24)*n^4 - (1/12)*n^3 + (11/24)*n^2 + (31/12)*n

k=3: [polynomial of degree 9] for n>2

k=4: [polynomial of degree 19] for n>6

k=5: [polynomial of degree 39] for n>14

EXAMPLE

Some solutions for n=4 k=4

..1..0..0..0....1..1..0..0....1..1..1..0....1..0..0..0....1..1..1..1

..1..0..0..1....0..0..0..0....1..0..0..0....0..0..0..1....1..1..0..0

..1..0..0..1....0..0..0..1....1..0..0..0....0..0..0..0....0..0..0..0

..0..0..0..1....0..1..1..0....1..0..0..0....0..0..1..0....0..0..0..0

CROSSREFS

Sequence in context: A239361 A266362 A241956 * A248944 A267245 A266428

Adjacent sequences:  A227122 A227123 A227124 * A227126 A227127 A227128

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Jul 01 2013

STATUS

approved

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Last modified June 15 16:13 EDT 2019. Contains 324142 sequences. (Running on oeis4.)