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%I #10 Aug 11 2015 09:18:18
%S 322,694,1592,3886,9914,26224,71322,198318,561212,1611002,4679574,
%T 13730612,40642206,121238834,364209520,1101127798,3348686298,
%U 10239114144,31464490330,97136312190,301153069996,937321265322,2927816428982
%N Number of (n+1) X (3+1) 0..3 arrays with every 2 X 2 subblock summing to 6 and no 2 X 2 subblock having exactly two nonzero entries.
%C Column 3 of A251236.
%H R. H. Hardin, <a href="/A251231/b251231.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 13*a(n-1) -63*a(n-2) +122*a(n-3) +13*a(n-4) -371*a(n-5) +317*a(n-6) +308*a(n-7) -370*a(n-8) -144*a(n-9) +128*a(n-10) +48*a(n-11).
%e Some solutions for n=4:
%e ..1..1..0..1....0..2..1..2....3..1..1..2....1..3..1..3....0..1..1..3
%e ..1..3..2..3....2..2..1..2....1..1..3..0....1..1..1..1....3..2..2..0
%e ..2..0..1..0....1..1..2..1....3..1..1..2....1..3..1..3....1..0..2..2
%e ..1..3..2..3....3..1..2..1....0..2..2..1....1..1..1..1....3..2..2..0
%e ..1..1..0..1....1..1..2..1....3..1..1..2....3..1..3..1....0..1..1..3
%Y Cf. A251236.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 30 2014