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

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

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