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%I #4 Mar 03 2016 12:05:35
%S 2,3,4,4,9,6,5,16,24,10,6,25,60,66,14,7,36,120,224,174,22,8,49,210,
%T 570,820,462,30,9,64,336,1212,2670,2976,1206,46,10,81,504,2282,6918,
%U 12390,10700,3150,62,11,100,720,3936,15358,39156,57030,38224,8166,94,12,121
%N T(n,k)=Number of length-n 0..k arrays with no repeated value differing from the previous repeated value by other than plus or minus one modulo k+1.
%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....66....224.....570.....1212......2282......3936.......6354.......9740
%C .14...174....820....2670.....6918.....15358.....30504......55710......95290
%C .22...462...2976...12390....39156....102606....234912.....485766.....927780
%C .30..1206..10700...57030...220050....681254...1799256....4215510....8995310
%C .46..3150..38224..260790..1229292...4499278..13716480...36430614...86891980
%C .62..8166.135780.1185990..6832518..29579382.104139336..313684470..836599530
%C .94.21150.480176.5368470.37810116.193688894.787814400.2692218006.8031245540
%H R. H. Hardin, <a href="/A269678/b269678.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)
%F k=3: a(n) = 5*a(n-1) -a(n-2) -15*a(n-3)
%F k=4: a(n) = 7*a(n-1) -6*a(n-2) -24*a(n-3)
%F k=5: a(n) = 9*a(n-1) -13*a(n-2) -35*a(n-3)
%F k=6: a(n) = 11*a(n-1) -22*a(n-2) -48*a(n-3)
%F k=7: a(n) = 13*a(n-1) -33*a(n-2) -63*a(n-3)
%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 + 2 for n>1
%F n=5: a(n) = n^5 + 5*n^4 + 4*n^3 + 6*n^2 + 4*n - 2 for n>1
%F n=6: a(n) = n^6 + 6*n^5 + 5*n^4 + 12*n^3 + 6*n^2 + 6 for n>1
%F n=7: a(n) = n^7 + 7*n^6 + 6*n^5 + 20*n^4 + 8*n^3 + 10*n^2 + 12*n - 10 for n>1
%e Some solutions for n=6 k=4
%e ..0. .1. .4. .0. .2. .4. .0. .4. .4. .4. .4. .4. .3. .0. .4. .4
%e ..2. .3. .2. .3. .3. .1. .0. .2. .4. .2. .0. .3. .3. .3. .0. .2
%e ..0. .2. .4. .2. .4. .3. .4. .1. .0. .3. .3. .2. .0. .0. .3. .3
%e ..3. .3. .1. .1. .1. .4. .1. .2. .2. .3. .2. .1. .4. .4. .3. .4
%e ..0. .3. .3. .0. .4. .2. .0. .3. .0. .2. .1. .0. .3. .4. .4. .1
%e ..1. .2. .4. .2. .4. .2. .4. .1. .4. .0. .2. .1. .4. .3. .2. .3
%Y Column 1 is A027383.
%Y Column 2 is A269461.
%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_, Mar 03 2016
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