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A269605 Number of length-n 0..7 arrays with no repeated value differing from the previous repeated value by one or less.

%I A269605 #7 Jan 24 2019 15:28:23
%S A269605 8,64,504,3962,31024,242226,1886252,14654952,113629480,879470154,
%T A269605 6796127732,52443005888,404170590152,3111359345068,23927329547328,
%U A269605 183840499514208,1411335451447128,10826702362761906,82998453154738884
%N A269605 Number of length-n 0..7 arrays with no repeated value differing from the previous repeated value by one or less.
%C A269605 Column 7 of A269606.
%H A269605 R. H. Hardin, <a href="/A269605/b269605.txt">Table of n, a(n) for n = 1..210</a>
%H A269605 Robert Israel, <a href="/A269605/a269605.pdf">Maple-assisted proof of empirical recursion</a>
%F A269605 Empirical: a(n) = 31*a(n-1) -353*a(n-2) +1601*a(n-3) -435*a(n-4) -14505*a(n-5) +7118*a(n-6) +65542*a(n-7) +66279*a(n-8) +19971*a(n-9)
%F A269605 Empirical formula verified: see link. - _Robert Israel_, Jan 24 2019
%e A269605 Some solutions for n=5
%e A269605 ..7. .4. .1. .3. .5. .2. .3. .4. .0. .1. .2. .3. .1. .5. .1. .0
%e A269605 ..0. .1. .2. .3. .6. .0. .6. .7. .2. .2. .4. .2. .0. .6. .5. .3
%e A269605 ..1. .1. .5. .7. .0. .6. .6. .5. .0. .6. .4. .1. .5. .0. .1. .5
%e A269605 ..7. .2. .2. .1. .6. .5. .0. .6. .0. .2. .2. .1. .6. .4. .5. .0
%e A269605 ..7. .0. .3. .4. .5. .0. .7. .6. .4. .6. .0. .2. .3. .2. .7. .0
%p A269605 with(LinearAlgebra):
%p A269605 T:= Matrix(72,72):
%p A269605 for x from 0 to 7 do
%p A269605   for v from 0 to 8 do
%p A269605     i:= 1 + x + 8*v;
%p A269605     for y in {$0..7} minus {x} do
%p A269605       T[i,1+y+8*v]:= 1;
%p A269605     od:
%p A269605     if abs(x-v) > 1 or v=8 then T[i,1+x+8*x]:= 1 fi
%p A269605 od od:
%p A269605 u:= Vector([0$64,1$8]): v:= Vector(72,1):
%p A269605 Tv[1]:= v:
%p A269605 for n from 2 to 50 do Tv[n]:= T . Tv[n-1] od:
%p A269605 seq(u^%T . Tv[n], n=1..50); # _Robert Israel_, Jan 24 2019
%Y A269605 Cf. A269606.
%K A269605 nonn
%O A269605 1,1
%A A269605 _R. H. Hardin_, Mar 01 2016