A235679 - OEIS

%I #4 Jan 13 2014 10:54:50

%S 16,58,58,208,380,208,742,2456,2456,742,2644,15790,28584,15790,2644,

%T 9418,101398,330840,330840,101398,9418,33544,650928,3824528,6894210,

%U 3824528,650928,33544,119470,4178316,44196144,143484144,143484144,44196144

%N T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with the difference between each 2X2 subblock maximum and minimum lexicographically nondecreasing columnwise and nonincreasing rowwise

%C Table starts

%C ......16.........58..........208.............742...............2644

%C ......58........380.........2456...........15790.............101398

%C .....208.......2456........28584..........330840............3824528

%C .....742......15790.......330840.........6894210..........143484144

%C ....2644.....101398......3824528.......143484144.........5376199876

%C ....9418.....650928.....44196144......2985166430.......201368802704

%C ...33544....4178316....510685176.....62100488254......7541722428052

%C ..119470...26820102...5900818062...1291848133836....282448223982692

%C ..425500..172154058..68181837738..26873571586520..10578025710796398

%C .1515442.1105028596.787815537064.559034577488572.396159194076516486

%H R. H. Hardin, <a href="/A235679/b235679.txt">Table of n, a(n) for n = 1..220</a>

%F Empirical for column k:

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

%F k=2: a(n) = 8*a(n-1) -9*a(n-2) -9*a(n-3) +10*a(n-4) +3*a(n-5) -2*a(n-6)

%F k=3: [order 11]

%F k=4: [order 22]

%F k=5: [order 46]

%F k=6: [order 87]

%e Some solutions for n=3 k=4

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

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

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

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

%Y Column 1 is A180143(n+1)

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Jan 13 2014