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%I #4 Feb 28 2016 06:41:49
%S 2,3,4,4,9,8,5,16,27,14,6,25,64,77,24,7,36,125,250,215,40,8,49,216,
%T 617,964,591,66,9,64,343,1286,3021,3680,1609,108,10,81,512,2389,7616,
%U 14695,13946,4353,176,11,100,729,4082,16579,44904,71115,52562,11731,286,12,121
%N T(n,k)=Number of length-n 0..k arrays with no repeated value differing from the previous repeated value by 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 ...8....27.....64.....125......216.......343........512........729.......1000
%C ..14....77....250.....617.....1286......2389.......4082.......6545.......9982
%C ..24...215....964....3021.....7616.....16579......32460......58649......99496
%C ..40...591...3680...14695....44904....114695.....257536.....524655.....990440
%C ..66..1609..13946...71115...263794....791381....2039274....4686391....9847970
%C .108..4353..52562..342749..1545030...5448185...16120298...41805237...97817054
%C .176.11731.197288.1646513..9026500..37435583..127240496..372491293..970685708
%C .286.31543.738190.7888637.52624694.256804141.1003029086.3315522725.9624545062
%H R. H. Hardin, <a href="/A269494/b269494.txt">Table of n, a(n) for n = 1..9999</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1) -a(n-3)
%F k=2: a(n) = 6*a(n-1) -9*a(n-2) -4*a(n-3) +10*a(n-4) +4*a(n-5)
%F k=3: a(n) = 9*a(n-1) -24*a(n-2) +9*a(n-3) +26*a(n-4) +3*a(n-5)
%F k=4: a(n) = 12*a(n-1) -43*a(n-2) +24*a(n-3) +75*a(n-4) +20*a(n-5) -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 + 3*n + 1
%F n=4: a(n) = n^4 + 4*n^3 + 6*n^2 + 2*n + 1
%F n=5: a(n) = n^5 + 5*n^4 + 10*n^3 + 4*n^2 + 3*n + 1
%F n=6: a(n) = n^6 + 6*n^5 + 15*n^4 + 8*n^3 + 5*n^2 + 6*n - 1
%F n=7: a(n) = n^7 + 7*n^6 + 21*n^5 + 15*n^4 + 7*n^3 + 17*n^2 - n - 1
%e Some solutions for n=6 k=4
%e ..1. .0. .1. .0. .1. .4. .2. .2. .0. .0. .1. .2. .1. .0. .3. .2
%e ..1. .4. .0. .3. .2. .2. .4. .1. .2. .2. .1. .4. .0. .1. .2. .0
%e ..0. .4. .4. .2. .3. .1. .1. .4. .3. .2. .1. .0. .4. .3. .4. .0
%e ..1. .2. .1. .0. .2. .3. .4. .3. .1. .2. .1. .4. .1. .4. .4. .1
%e ..1. .0. .3. .3. .3. .4. .0. .1. .2. .4. .2. .3. .0. .2. .2. .2
%e ..4. .2. .2. .4. .2. .0. .1. .3. .3. .1. .3. .0. .2. .0. .1. .0
%Y Column 1 is A019274(n+2).
%Y Row 1 is A000027(n+1).
%Y Row 2 is A000290(n+1).
%Y Row 3 is A000578(n+1).
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Feb 28 2016
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