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T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock summing to 3 4 or 5
8

%I #4 Dec 01 2014 19:48:01

%S 51,309,309,1899,3921,1899,11709,50831,50831,11709,72243,663307,

%T 1401453,663307,72243,445797,8671957,39019417,39019417,8671957,445797,

%U 2751003,113445117,1089569635,2324761359,1089569635,113445117,2751003,16976493

%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock summing to 3 4 or 5

%C Table starts

%C .....51.......309........1899.........11709............72243.............445797

%C ....309......3921.......50831........663307..........8671957..........113445117

%C ...1899.....50831.....1401453......39019417.......1089569635........30455338423

%C ..11709....663307....39019417....2324761359.....139048718681......8328173688589

%C ..72243...8671957..1089569635..139048718681...17831423507215...2290637311033759

%C .445797.113445117.30455338423.8328173688589.2290637311033759.631348219277725029

%H R. H. Hardin, <a href="/A251351/b251351.txt">Table of n, a(n) for n = 1..144</a>

%F Empirical for column k:

%F k=1: a(n) = 6*a(n-1) +3*a(n-2) -12*a(n-3)

%F k=2: [order 7]

%F k=3: [order 21]

%F k=4: [order 60]

%e Some solutions for n=2 k=4

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 01 2014