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Number of length-n 0..4 arrays with no repeated value greater than or equal to the previous repeated value.
1

%I #8 Jan 21 2019 10:08:05

%S 5,25,120,570,2670,12380,56890,259445,1175355,5293671,23718780,

%T 105781845,469798125,2078552055,9164402118,40277785365,176503698495,

%U 771372344695,3362640467600,14624384170213,63463229049585,274836205944615

%N Number of length-n 0..4 arrays with no repeated value greater than or equal to the previous repeated value.

%H R. H. Hardin, <a href="/A269405/b269405.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 20*a(n-1) - 150*a(n-2) + 460*a(n-3) - 65*a(n-4) - 2472*a(n-5) + 2320*a(n-6) + 6400*a(n-7) - 3840*a(n-8) - 10240*a(n-9) - 4096*a(n-10).

%F Empirical g.f.: x*(5 - 75*x + 370*x^2 - 380*x^3 - 1905*x^4 + 3265*x^5 + 5590*x^6 - 5865*x^7 - 11455*x^8 - 4339*x^9) / ((1 + x)^4*(1 - 4*x)^6). - _Colin Barker_, Jan 21 2019

%e Some solutions for n=7:

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

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

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

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

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

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

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

%Y Column 4 of A269409

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 25 2016