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Number of (n+1)X(4+1) 0..3 arrays with the sum of all four elements of every 2X2 subblock equal
1

%I #4 Feb 02 2014 07:55:46

%S 5984,10776,20776,46416,108824,282048,755752,2169408,6387224,19785696,

%T 62577256,205965696,689940824,2386495968,8375807272,30155605248,

%U 109803847064,407743384416,1526506024936,5798829806976,22150030731224

%N Number of (n+1)X(4+1) 0..3 arrays with the sum of all four elements of every 2X2 subblock equal

%C Column 4 of A237015

%H R. H. Hardin, <a href="/A237011/b237011.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 8*a(n-1) +16*a(n-2) -268*a(n-3) +189*a(n-4) +3388*a(n-5) -5824*a(n-6) -20048*a(n-7) +49756*a(n-8) +52752*a(n-9) -196896*a(n-10) -24192*a(n-11) +369216*a(n-12) -131328*a(n-13) -262656*a(n-14) +165888*a(n-15)

%e Some solutions for n=5

%e ..0..3..1..2..1....2..1..1..2..3....2..2..2..1..1....2..0..3..1..3

%e ..3..2..2..3..2....2..1..3..0..1....1..1..1..2..2....3..2..2..1..2

%e ..0..3..1..2..1....2..1..1..2..3....2..2..2..1..1....0..2..1..3..1

%e ..3..2..2..3..2....2..1..3..0..1....2..0..2..1..3....3..2..2..1..2

%e ..1..2..2..1..2....2..1..1..2..3....1..3..1..2..0....1..1..2..2..2

%e ..3..2..2..3..2....2..1..3..0..1....2..0..2..1..3....3..2..2..1..2

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 02 2014