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%I #4 May 17 2014 19:22:13
%S 7,13,12,14,35,21,14,45,97,37,14,46,159,271,65,14,46,174,587,757,114,
%T 14,46,175,723,2209,2115,200,14,46,175,744,3192,8391,5913,351,14,46,
%U 175,745,3453,14648,32020,16535,616,14,46,175,745,3481,17178,68819,122439,46237
%N T(n,k)=Number of length n+3 0..k arrays with no four elements in a row with pattern aabb (with a!=b) and new values 0..k introduced in 0..k order
%C Table starts
%C ....7.....13......14......14.......14.......14.......14.......14.......14
%C ...12.....35......45......46.......46.......46.......46.......46.......46
%C ...21.....97.....159.....174......175......175......175......175......175
%C ...37....271.....587.....723......744......745......745......745......745
%C ...65....757....2209....3192.....3453.....3481.....3482.....3482.....3482
%C ..114...2115....8391...14648....17178....17634....17670....17671....17671
%C ..200...5913...32020...68819....90033....95729....96472....96517....96518
%C ..351..16535..122439..327821...489821...550503...562109...563256...563311
%C ..616..46237..468605.1574161..2734513..3316400..3469255..3491141..3492837
%C .1081.129291.1794215.7594177.15534111.20716789.22511261.22860029.22898822
%H R. H. Hardin, <a href="/A242584/b242584.txt">Table of n, a(n) for n = 1..9999</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3)
%F k=2: a(n) = 4*a(n-1) -5*a(n-2) +6*a(n-3) -4*a(n-4)
%F k=3: a(n) = 7*a(n-1) -18*a(n-2) +32*a(n-3) -45*a(n-4) +37*a(n-5) -21*a(n-6) +9*a(n-7)
%F k=4: [order 10]
%F k=5: [order 13]
%F k=6: [order 16]
%F k=7: [order 19]
%e Some solutions for n=4 k=4
%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e ..1....1....1....1....1....1....1....1....1....1....1....0....1....1....1....1
%e ..0....2....0....2....2....2....2....2....2....2....2....1....1....2....2....2
%e ..2....1....2....2....3....0....0....3....3....1....3....2....1....1....0....2
%e ..1....2....0....0....4....3....3....0....3....0....4....3....2....3....2....3
%e ..3....3....0....3....1....3....2....4....3....3....3....2....1....3....3....4
%e ..2....2....3....4....2....4....4....3....2....1....3....1....2....0....4....0
%Y Column 1 is A005251(n+5)
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, May 17 2014