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%I #11 Aug 10 2015 17:56:32
%S 38,110,110,322,270,322,966,694,694,966,2930,1870,1592,1870,2930,8982,
%T 5194,3886,3886,5194,8982,27714,14786,9914,8686,9914,14786,27714,
%U 85958,42850,26224,20490,20490,26224,42850,85958,267602,125934,71322,50570
%N T(n,k) = Number of (n+1) X (k+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 Table starts:
%C .....38.....110.....322.....966....2930....8982....27714....85958...267602
%C ....110.....270.....694....1870....5194...14786....42850...125934...374166
%C ....322.....694....1592....3886....9914...26224....71322...198318...561212
%C ....966....1870....3886....8686...20490...50570...129378...340782...918878
%C ...2930....5194....9914...20490...44966..103926...250622...626122..1610186
%C ...8982...14786...26224...50570..103926..225936...514950..1222090..3000620
%C ..27714...42850...71322..129378..250622..514950..1112526..2511890..5892002
%C ..85958..125934..198318..340782..626122.1222090..2511890..5407182.12127278
%C .267602..374166..561212..918878.1610186.3000620..5892002.12127278
%C .835574.1121566.1611002.2525262.4240330.7579486.14279706
%H R. H. Hardin, <a href="/A251236/b251236.txt">Table of n, a(n) for n = 1..144</a>
%F Empirical for column k (k=3 recurrence works also for k=1 and k=2):
%F k=1: a(n) = 7*a(n-1) -12*a(n-2) -8*a(n-3) +24*a(n-4)
%F k=2: [order 9]
%F k=3: [order 11]
%F k=4: [same order 11]
%F k=5: [same order 11]
%F k=6: [same order 11]
%F k=7: [same order 11]
%e Some solutions for n=4, k=4:
%e ..0..2..0..2..1....1..1..1..2..1....1..2..3..2..3....3..1..2..0..3
%e ..1..3..1..3..0....1..3..1..2..1....3..0..1..0..1....2..0..3..1..2
%e ..0..2..0..2..1....0..2..0..3..0....1..2..3..2..3....2..2..1..1..2
%e ..1..3..1..3..0....1..3..1..2..1....3..0..1..0..1....1..1..2..2..1
%e ..0..2..0..2..1....1..1..1..2..1....1..2..3..2..3....2..2..1..1..2
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Nov 30 2014