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%I #4 Feb 16 2016 06:36:55
%S 2,3,4,4,9,6,5,16,24,10,6,25,60,63,14,7,36,120,220,159,22,8,49,210,
%T 565,788,396,30,9,64,336,1206,2615,2780,969,46,10,81,504,2275,6834,
%U 11950,9684,2349,62,11,100,720,3928,15239,38322,54045,33404,5640,94,12,121,990
%N T(n,k)=Number of length-n 0..k arrays with no repeated value unequal to the previous repeated value plus one mod 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....63....220.....565.....1206......2275......3928.......6345.......9730
%C .14...159....788....2615.....6834.....15239.....30344......55503......95030
%C .22...396...2780...11950....38322....101192....232696.....482490.....923150
%C .30...969...9684...54045...213042....667065...1773384....4171869....8925990
%C .46..2349..33404..242365..1175850...4370261..13443064...35904789...85953830
%C .62..5640.114292.1079240..6450402..28480312.101433800..307754712..824720230
%C .94.13455.388444.4777225.35200458.184750699.762265720.2628421029.7887767350
%H R. H. Hardin, <a href="/A268944/b268944.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) +a(n-2) -6*a(n-3)
%F k=3: a(n) = 5*a(n-1) -2*a(n-2) -12*a(n-3)
%F k=4: a(n) = 7*a(n-1) -7*a(n-2) -20*a(n-3)
%F k=5: a(n) = 9*a(n-1) -14*a(n-2) -30*a(n-3)
%F k=6: a(n) = 11*a(n-1) -23*a(n-2) -42*a(n-3)
%F k=7: a(n) = 13*a(n-1) -34*a(n-2) -56*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 + n + 1
%F n=5: a(n) = n^5 + 5*n^4 + 4*n^3 + 3*n^2 + 2*n - 1
%F n=6: a(n) = n^6 + 6*n^5 + 5*n^4 + 6*n^3 + 3*n^2 - n + 2
%F n=7: a(n) = n^7 + 7*n^6 + 6*n^5 + 10*n^4 + 4*n^3 + n^2 + 4*n - 3
%e Some solutions for n=6 k=4
%e ..2. .4. .3. .1. .4. .4. .1. .2. .2. .0. .4. .2. .0. .3. .2. .3
%e ..1. .4. .3. .0. .1. .0. .2. .3. .4. .0. .0. .1. .3. .0. .2. .3
%e ..1. .2. .2. .1. .3. .4. .4. .0. .2. .2. .2. .2. .0. .2. .3. .1
%e ..2. .4. .4. .3. .4. .0. .1. .2. .4. .1. .1. .3. .1. .0. .4. .2
%e ..3. .0. .2. .0. .2. .1. .2. .3. .1. .0. .0. .0. .1. .3. .0. .0
%e ..2. .3. .0. .0. .4. .4. .0. .4. .2. .2. .1. .2. .4. .3. .2. .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 16 2016
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