%I #4 Feb 29 2016 07:04:50
%S 2,3,4,4,9,6,5,16,24,10,6,25,60,64,14,7,36,120,222,164,22,8,49,210,
%T 568,804,418,30,9,64,336,1210,2648,2878,1048,46,10,81,504,2280,6890,
%U 12214,10192,2614,62,11,100,720,3934,15324,38878,55836,35812,6468,94,12,121
%N T(n,k)=Number of length-n 0..k arrays with no repeated value differing from the previous repeated value by other than one.
%C Table starts
%C ..2.....3......4.......5........6.........7.........8..........9.........10
%C ..4.....9.....16......25.......36........49........64.........81........100
%C ..6....24.....60.....120......210.......336.......504........720........990
%C .10....64....222.....568.....1210......2280......3934.......6352.......9738
%C .14...164....804....2648.....6890.....15324.....30464......55664......95238
%C .22...418...2878...12214....38878....102202....234358.....485038.....926854
%C .30..1048..10192...55836...217714....677200...1792788....4205812....8981446
%C .46..2614..35812..253418..1211476...4462414..13648124...36313762...86704348
%C .62..6468.125012.1143256..6705102..29265308.103462888..312366672..834223586
%C .94.15942.434110.5131592.36939610.191134204.781425950.2678039200.8002547722
%H R. H. Hardin, <a href="/A269537/b269537.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) = 4*a(n-1) -a(n-2) -10*a(n-3) +6*a(n-4) +4*a(n-5)
%F k=3: a(n) = 7*a(n-1) -9*a(n-2) -23*a(n-3) +31*a(n-4) +33*a(n-5)
%F k=4: a(n) = 14*a(n-1) -65*a(n-2) +80*a(n-3) +163*a(n-4) -280*a(n-5) -208*a(n-6)
%F k=5: [order 7]
%F k=6: [order 9]
%F k=7: [order 9]
%F Empirical for row n:
%F n=1: a(n) = n + 1
%F n=2: a(n) = n^2 + 2*n + 1
%F n=3: a(n) = n^3 + 3*n^2 + 2*n
%F n=4: a(n) = n^4 + 4*n^3 + 3*n^2 + 2*n
%F n=5: a(n) = n^5 + 5*n^4 + 4*n^3 + 6*n^2 - 2*n
%F n=6: a(n) = n^6 + 6*n^5 + 5*n^4 + 12*n^3 - 6*n^2 + 6*n - 2
%F n=7: a(n) = n^7 + 7*n^6 + 6*n^5 + 20*n^4 - 12*n^3 + 22*n^2 - 18*n + 4
%e Some solutions for n=6 k=4
%e ..2. .4. .4. .0. .3. .0. .0. .3. .1. .2. .2. .3. .2. .1. .4. .0
%e ..4. .3. .1. .3. .2. .2. .3. .0. .2. .0. .1. .0. .1. .3. .0. .2
%e ..3. .2. .0. .1. .1. .4. .1. .0. .3. .3. .3. .1. .3. .0. .4. .2
%e ..2. .1. .1. .2. .1. .0. .3. .2. .3. .4. .1. .0. .4. .2. .1. .4
%e ..0. .3. .1. .2. .0. .1. .1. .4. .2. .1. .1. .1. .1. .4. .1. .0
%e ..2. .1. .2. .4. .2. .1. .2. .0. .0. .2. .2. .2. .3. .2. .4. .4
%Y Column 1 is A027383.
%Y Row 1 is A000027(n+1).
%Y Row 2 is A000290(n+1).
%Y Row 3 is A007531(n+2).
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Feb 29 2016