A268956 - OEIS

%I #4 Feb 16 2016 11:51:33

%S 1,1,2,1,2,3,1,2,4,5,1,2,4,11,7,1,2,4,12,29,11,1,2,4,12,39,77,15,1,2,

%T 4,12,40,138,201,23,1,2,4,12,40,153,499,525,31,1,2,4,12,40,154,634,

%U 1830,1361,47,1,2,4,12,40,154,655,2785,6723,3525,63,1,2,4,12,40,154,656,3045

%N T(n,k)=Number of length-n 0..k arrays with no repeated value equal to the previous repeated value, with new values introduced in sequential order.

%C Table starts

%C ..1....1.....1.....1.....1.....1.....1.....1.....1.....1.....1.....1.....1

%C ..2....2.....2.....2.....2.....2.....2.....2.....2.....2.....2.....2.....2

%C ..3....4.....4.....4.....4.....4.....4.....4.....4.....4.....4.....4.....4

%C ..5...11....12....12....12....12....12....12....12....12....12....12....12

%C ..7...29....39....40....40....40....40....40....40....40....40....40....40

%C .11...77...138...153...154...154...154...154...154...154...154...154...154

%C .15..201...499...634...655...656...656...656...656...656...656...656...656

%C .23..525..1830..2785..3045..3073..3074..3074..3074..3074..3074..3074..3074

%C .31.1361..6723.12634.15124.15579.15615.15616.15616.15616.15616.15616.15616

%C .47.3525.24714.58409.78930.84572.85314.85359.85360.85360.85360.85360.85360

%H R. H. Hardin, <a href="/A268956/b268956.txt">Table of n, a(n) for n = 1..9999</a>

%F Empirical for column k:

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

%F k=2: a(n) = 3*a(n-1) +2*a(n-2) -8*a(n-3) for n>5

%F k=3: a(n) = 6*a(n-1) -3*a(n-2) -30*a(n-3) +28*a(n-4) +36*a(n-5) -36*a(n-6) for n>8

%F k=4: [order 9] for n>11

%F k=5: [order 12] for n>14

%F k=6: [order 15] for n>17

%F k=7: [order 18] for n>20

%e Some solutions for n=8 k=4

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

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

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

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

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

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

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

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

%Y Column 1 is A052955(n-1).

%Y Column 2 is A267912.

%Y Column 3 is A268069.

%Y Diagonal is A268010.

%K nonn,tabl

%O 1,3

%A _R. H. Hardin_, Feb 16 2016