cp's OEIS Frontend

A268956 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.

%I A268956 #4 Feb 16 2016 11:51:33
%S A268956 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 A268956 4,12,40,138,201,23,1,2,4,12,40,153,499,525,31,1,2,4,12,40,154,634,
%U A268956 1830,1361,47,1,2,4,12,40,154,655,2785,6723,3525,63,1,2,4,12,40,154,656,3045
%N A268956 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 A268956 Table starts
%C A268956 ..1....1.....1.....1.....1.....1.....1.....1.....1.....1.....1.....1.....1
%C A268956 ..2....2.....2.....2.....2.....2.....2.....2.....2.....2.....2.....2.....2
%C A268956 ..3....4.....4.....4.....4.....4.....4.....4.....4.....4.....4.....4.....4
%C A268956 ..5...11....12....12....12....12....12....12....12....12....12....12....12
%C A268956 ..7...29....39....40....40....40....40....40....40....40....40....40....40
%C A268956 .11...77...138...153...154...154...154...154...154...154...154...154...154
%C A268956 .15..201...499...634...655...656...656...656...656...656...656...656...656
%C A268956 .23..525..1830..2785..3045..3073..3074..3074..3074..3074..3074..3074..3074
%C A268956 .31.1361..6723.12634.15124.15579.15615.15616.15616.15616.15616.15616.15616
%C A268956 .47.3525.24714.58409.78930.84572.85314.85359.85360.85360.85360.85360.85360
%H A268956 R. H. Hardin, <a href="/A268956/b268956.txt">Table of n, a(n) for n = 1..9999</a>
%F A268956 Empirical for column k:
%F A268956 k=1: a(n) = a(n-1) +2*a(n-2) -2*a(n-3)
%F A268956 k=2: a(n) = 3*a(n-1) +2*a(n-2) -8*a(n-3) for n>5
%F A268956 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 A268956 k=4: [order 9] for n>11
%F A268956 k=5: [order 12] for n>14
%F A268956 k=6: [order 15] for n>17
%F A268956 k=7: [order 18] for n>20
%e A268956 Some solutions for n=8 k=4
%e A268956 ..0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0
%e A268956 ..1. .1. .1. .0. .1. .1. .1. .1. .1. .1. .1. .1. .1. .1. .1. .1
%e A268956 ..2. .2. .2. .1. .2. .2. .0. .1. .1. .2. .2. .2. .2. .0. .2. .2
%e A268956 ..2. .3. .2. .0. .3. .3. .2. .2. .2. .1. .2. .3. .1. .1. .0. .1
%e A268956 ..1. .4. .3. .2. .4. .2. .1. .3. .3. .3. .3. .1. .0. .2. .0. .3
%e A268956 ..1. .3. .4. .1. .4. .2. .3. .0. .3. .3. .3. .4. .2. .1. .3. .4
%e A268956 ..2. .2. .0. .2. .3. .4. .0. .1. .1. .1. .2. .0. .0. .2. .1. .2
%e A268956 ..0. .0. .0. .3. .1. .1. .3. .2. .4. .3. .1. .0. .0. .1. .0. .2
%Y A268956 Column 1 is A052955(n-1).
%Y A268956 Column 2 is A267912.
%Y A268956 Column 3 is A268069.
%Y A268956 Diagonal is A268010.
%K A268956 nonn,tabl
%O A268956 1,3
%A A268956 _R. H. Hardin_, Feb 16 2016