A244185 - OEIS

%I #4 Jun 21 2014 21:31:22

%S 13,38,22,48,108,36,49,173,306,59,49,188,650,867,97,49,189,790,2495,

%T 2457,160,49,189,811,3537,9667,6963,263,49,189,812,3803,16477,37604,

%U 19732,433,49,189,812,3831,19113,78614,146521,55918,712,49,189,812,3832,19575

%N T(n,k)=Number of length n+4 0..k arrays with no five consecutive elements with pattern ababa or abbba (possibly a=b) and new values 0..k introduced in 0..k order

%C Table starts

%C ...13.....38......48.......49........49........49........49........49........49

%C ...22....108.....173......188.......189.......189.......189.......189.......189

%C ...36....306.....650......790.......811.......812.......812.......812.......812

%C ...59....867....2495.....3537......3803......3831......3832......3832......3832

%C ...97...2457....9667....16477.....19113.....19575.....19611.....19612.....19612

%C ..160...6963...37604....78614....101200....107068....107818....107863....107864

%C ..263..19732..146521...380407....556443....620051....631917....633072....633127

%C ..433..55918..571315..1855983...3141344...3761768...3920234...3942493...3944198

%C ..712.158464.2228340..9098538..18055451..23672967..25559691..25918400..25957707

%C .1172.449066.8692454.44726540.105031051.153195068.173884143.178997028.179748699

%H R. H. Hardin, <a href="/A244185/b244185.txt">Table of n, a(n) for n = 1..4239</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-2) +a(n-3) +2*a(n-4) +a(n-5) +a(n-6)

%F k=2: a(n) = a(n-1) +3*a(n-2) +4*a(n-3) +5*a(n-4) +3*a(n-5) +2*a(n-6)

%F k=3: [order 12]

%F k=4: [order 18]

%F k=5: [order 24]

%F k=6: [order 30]

%F k=7: [order 36]

%F k=8: [order 42]

%F k=9: [order 48]

%e Some solutions for n=6 k=4

%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

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

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

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

%e ..2....2....4....1....3....0....2....3....3....0....2....2....3....2....1....0

%e ..3....1....4....2....0....1....3....3....3....0....3....0....4....3....0....3

%e ..0....0....3....0....0....3....2....4....4....0....2....3....3....0....2....1

%e ..0....0....2....0....4....4....1....4....0....4....1....0....3....1....3....4

%e ..2....0....2....1....3....4....4....2....2....2....2....1....1....3....1....1

%e ..3....0....0....2....0....1....0....1....1....0....4....1....1....4....1....2

%Y Column 1 is A164441(n+3)

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Jun 21 2014