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A269619 T(n,k)=Number of length-n 0..k arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.

%I A269619 #4 Mar 01 2016 14:57:21
%S A269619 2,3,4,4,9,8,5,16,27,15,6,25,64,78,28,7,36,125,249,222,51,8,49,216,
%T A269619 612,954,624,92,9,64,343,1275,2956,3611,1740,164,10,81,512,2370,7440,
%U A269619 14125,13544,4824,290,11,100,729,4053,16218,43013,66925,50442,13320,509,12,121
%N A269619 T(n,k)=Number of length-n 0..k arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.
%C A269619 Table starts
%C A269619 ...2.....3......4.......5........6.........7.........8..........9.........10
%C A269619 ...4.....9.....16......25.......36........49........64.........81........100
%C A269619 ...8....27.....64.....125......216.......343.......512........729.......1000
%C A269619 ..15....78....249.....612.....1275......2370......4053.......6504.......9927
%C A269619 ..28...222....954....2956.....7440.....16218.....31822......57624......97956
%C A269619 ..51...624...3611...14125....43013....110099....248143.....507521.....961625
%C A269619 ..92..1740..13544...66925...246798....742487...1923796....4447329....9398090
%C A269619 .164..4824..50442..314935..1407232...4979260..14840928...38800210...91490344
%C A269619 .290.13320.186822.1473779..7982022..33232924.113998742..337209090..887591878
%C A269619 .509.36672.688899.6865098.45074673.220896016.872397577.2920747321.8584628259
%H A269619 R. H. Hardin, <a href="/A269619/b269619.txt">Table of n, a(n) for n = 1..9999</a>
%F A269619 Empirical for column k:
%F A269619 k=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4)
%F A269619 k=2: a(n) = 4*a(n-1) -2*a(n-2) -4*a(n-3)
%F A269619 k=3: a(n) = 12*a(n-1) -51*a(n-2) +81*a(n-3) -3*a(n-4) -63*a(n-5) -24*a(n-6) -9*a(n-7)
%F A269619 k=4: [order 7]
%F A269619 k=5: [order 13]
%F A269619 k=6: [order 15]
%F A269619 k=7: [order 17]
%F A269619 Empirical for row n:
%F A269619 n=1: a(n) = n + 1
%F A269619 n=2: a(n) = n^2 + 2*n + 1
%F A269619 n=3: a(n) = n^3 + 3*n^2 + 3*n + 1
%F A269619 n=4: a(n) = n^4 + 4*n^3 + 5*n^2 + 5*n
%F A269619 n=5: a(n) = n^5 + 5*n^4 + 7*n^3 + 12*n^2 + 3*n
%F A269619 n=6: a(n) = n^6 + 6*n^5 + 9*n^4 + 22*n^3 + 9*n^2 + 9*n - 7 for n>2
%F A269619 n=7: a(n) = n^7 + 7*n^6 + 11*n^5 + 35*n^4 + 18*n^3 + 36*n^2 - 19*n - 7 for n>2
%e A269619 Some solutions for n=6 k=4
%e A269619 ..1. .2. .0. .2. .1. .4. .3. .4. .2. .2. .0. .2. .2. .2. .2. .0
%e A269619 ..0. .3. .3. .1. .4. .0. .0. .0. .2. .1. .0. .1. .0. .2. .4. .3
%e A269619 ..4. .3. .2. .1. .1. .3. .0. .4. .1. .0. .4. .3. .1. .2. .4. .1
%e A269619 ..3. .3. .2. .2. .4. .2. .4. .0. .3. .3. .0. .3. .4. .3. .3. .1
%e A269619 ..0. .3. .1. .3. .0. .1. .3. .4. .1. .1. .2. .1. .4. .1. .4. .1
%e A269619 ..0. .3. .0. .4. .4. .1. .4. .2. .1. .0. .1. .0. .3. .4. .2. .2
%Y A269619 Column 1 is A029907(n+1).
%Y A269619 Row 1 is A000027(n+1).
%Y A269619 Row 2 is A000290(n+1).
%Y A269619 Row 3 is A000578(n+1).
%K A269619 nonn,tabl
%O A269619 1,1
%A A269619 _R. H. Hardin_, Mar 01 2016