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%I A269496 #8 Jan 23 2019 11:46:17
%S A269496 24,215,964,3021,7616,16579,32460,58649,99496,160431,248084,370405,
%T A269496 536784,758171,1047196,1418289,1887800,2474119,3197796,4081661,
%U A269496 5150944,6433395,7959404,9762121,11877576,14344799,17205940,20506389,24294896
%N A269496 Number of length-5 0..n arrays with no repeated value differing from the previous repeated value by one.
%H A269496 R. H. Hardin, <a href="/A269496/b269496.txt">Table of n, a(n) for n = 1..210</a>
%F A269496 Empirical: a(n) = n^5 + 5*n^4 + 10*n^3 + 4*n^2 + 3*n + 1.
%F A269496 Conjectures from _Colin Barker_, Jan 23 2019: (Start)
%F A269496 G.f.: x*(24 + 71*x + 34*x^2 - 18*x^3 + 10*x^4 - x^5) / (1 - x)^6.
%F A269496 a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6
%F A269496 (End)
%e A269496 Some solutions for n=6:
%e A269496 ..3. .0. .3. .3. .4. .2. .3. .4. .2. .6. .5. .4. .6. .1. .5. .5
%e A269496 ..5. .1. .3. .0. .6. .2. .3. .3. .1. .3. .4. .2. .2. .4. .1. .3
%e A269496 ..1. .6. .3. .1. .0. .5. .2. .4. .0. .4. .1. .0. .0. .5. .5. .6
%e A269496 ..6. .2. .4. .5. .6. .1. .4. .2. .4. .1. .0. .6. .1. .4. .3. .6
%e A269496 ..5. .5. .1. .6. .5. .5. .6. .3. .3. .5. .2. .1. .4. .1. .4. .5
%Y A269496 Row 5 of A269494.
%K A269496 nonn
%O A269496 1,1
%A A269496 _R. H. Hardin_, Feb 28 2016

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