A212829 - OEIS

%I #4 May 28 2012 08:36:13

%S 1,1,2,1,2,4,1,2,5,6,1,2,5,12,10,1,2,5,13,33,16,1,2,5,13,43,90,26,1,2,

%T 5,13,44,152,246,42,1,2,5,13,44,167,559,672,68,1,2,5,13,44,168,695,

%U 2091,1836,110,1,2,5,13,44,168,716,3070,7882,5016,178,1,2,5,13,44,168,717

%N T(n,k)=Number of 0..k arrays of length n with no adjacent pair equal to its immediately preceding adjacent pair, and new values introduced in 0..k order

%C Table starts

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

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

%C ...4.....5......5.......5.......5.......5.......5.......5.......5.......5

%C ...6....12.....13......13......13......13......13......13......13......13

%C ..10....33.....43......44......44......44......44......44......44......44

%C ..16....90....152.....167.....168.....168.....168.....168.....168.....168

%C ..26...246....559.....695.....716.....717.....717.....717.....717.....717

%C ..42...672...2091....3070....3331....3359....3360....3360....3360....3360

%C ..68..1836...7882...14074...16599...17055...17091...17092...17092...17092

%C .110..5016..29809...65958...87059...92749...93492...93537...93538...93538

%C .178.13704.112895..313098..473569..534071..545670..546817..546872..546873

%C .288.37440.427824.1497216.2641428.3220152.3372738.3394616.3396312.3396378

%H R. H. Hardin, <a href="/A212829/b212829.txt">Table of n, a(n) for n = 1..6054</a>

%F Empirical for column k:

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

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

%F k=3: a(n) = 4*a(n-1) +a(n-2) -6*a(n-3) -3*a(n-4) for n>7

%F k=4: a(n) = 7*a(n-1) -7*a(n-2) -20*a(n-3) +10*a(n-4) +24*a(n-5) +8*a(n-6) for n>9

%F k=5: a(n) = 11*a(n-1) -30*a(n-2) -21*a(n-3) +112*a(n-4) +63*a(n-5) -119*a(n-6) -120*a(n-7) -30*a(n-8) for n>11

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

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

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

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

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

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

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

%Y Column 1 is A128588

%K nonn,tabl

%O 1,3

%A _R. H. Hardin_ May 28 2012