A227125 - OEIS

%I #4 Jul 01 2013 20:43:07

%S 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,

%T 68,8,9,112,492,1079,1079,492,112,9,10,178,1143,3836,5820,3836,1143,

%U 178,10,11,273,2524,12954,30620,30620,12954,2524,273,11,12,405,5315,41334

%N 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

%C Table starts

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

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

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

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

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

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

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

%C ..9.178.2524..41334..732611.13289471..238464936..4109192774...67076312881

%C .10.273.5315.124956.3296920.90728418.2504527178.67076312881.1709864974106

%H R. H. Hardin, <a href="/A227125/b227125.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

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

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

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

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

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

%e Some solutions for n=4 k=4

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Jul 01 2013