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A269622 Number of length-6 0..n arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1. 1

%I #7 Jan 25 2019 08:27:48

%S 51,624,3611,14125,43013,110099,248143,507521,961625,1712983,2900099,

%T 4705013,7361581,11164475,16478903,23751049,33519233,46425791,

%U 63229675,84819773,112228949,146648803,189445151,242174225,306599593,384709799

%N Number of length-6 0..n arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.

%H R. H. Hardin, <a href="/A269622/b269622.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^6 + 6*n^5 + 9*n^4 + 22*n^3 + 9*n^2 + 9*n - 7 for n>2.

%F Conjectures from _Colin Barker_, Jan 25 2019: (Start)

%F G.f.: x*(51 + 267*x + 314*x^2 + 167*x^3 - 86*x^4 + 17*x^5 - 14*x^6 + 5*x^7 - x^8) / (1 - x)^7.

%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>9.

%F (End)

%e Some solutions for n=6:

%e ..1. .2. .0. .5. .3. .1. .1. .5. .3. .0. .5. .4. .0. .3. .0. .2

%e ..6. .2. .2. .0. .6. .4. .0. .1. .3. .5. .2. .1. .6. .2. .5. .4

%e ..3. .3. .0. .5. .3. .5. .1. .4. .3. .5. .4. .0. .5. .1. .5. .4

%e ..3. .1. .2. .2. .1. .4. .2. .3. .3. .4. .3. .3. .4. .4. .5. .0

%e ..6. .1. .6. .4. .4. .3. .5. .4. .2. .5. .6. .3. .1. .1. .4. .2

%e ..4. .3. .0. .3. .3. .0. .5. .4. .1. .5. .3. .1. .4. .2. .4. .5

%Y Row 6 of A269619.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 01 2016

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)