A237567 - OEIS

%I #4 Feb 09 2014 06:59:02

%S 81,316,316,1256,1536,1256,4984,7356,7356,4984,19900,36168,44828,

%T 36168,19900,78144,175768,272828,272828,175768,78144,311512,848720,

%U 1668300,2161168,1668300,848720,311512,1227648,4121060,10006572,16418704

%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with the upper median plus the lower median of every 2X2 subblock differing from its horizontal and vertical neighbors by exactly one

%C Table starts

%C .......81.......316........1256.........4984..........19900...........78144

%C ......316......1536........7356........36168.........175768..........848720

%C .....1256......7356.......44828.......272828........1668300........10006572

%C .....4984.....36168......272828......2161168.......16418704.......126608036

%C ....19900....175768.....1668300.....16418704......159014170......1518590620

%C ....78144....848720....10006572....126608036.....1518590620.....18615658788

%C ...311512...4121060....61521086....977290740....14891233160....228407442348

%C ..1227648..20050460...369916012...7535608804...142803584684...2815624842216

%C ..4896848..97225972..2269219612..58063606256..1403992115612..34622654326396

%C .19273664.471641072.13640047444.448289864392.13464379623752.426711928933956

%H R. H. Hardin, <a href="/A237567/b237567.txt">Table of n, a(n) for n = 1..127</a>

%F Empirical for column k:

%F k=1: a(n) = 4*a(n-2) +140*a(n-4) +632*a(n-6) +864*a(n-8) for n>9

%F k=2: [order 17]

%F k=3: [order 60] for n>63

%e Some solutions for n=3 k=4

%e ..1..0..0..1..1....0..0..1..0..1....0..2..2..1..2....0..1..1..2..2

%e ..0..1..0..2..1....0..0..1..1..0....1..2..2..1..0....0..2..0..2..1

%e ..2..1..0..2..1....1..1..2..2..1....0..1..1..1..0....0..2..1..1..2

%e ..2..1..2..1..0....0..2..0..0..2....0..1..0..0..0....2..1..0..0..1

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Feb 09 2014