cp's OEIS Frontend

A212825 Number of 0..4 arrays of length n with no adjacent pair equal to its immediately preceding adjacent pair, and new values introduced in 0..4 order.

%I A212825 #8 Jul 21 2018 10:06:34
%S A212825 1,2,5,13,44,167,695,3070,14074,65958,313098,1497216,7189646,34606966,
%T A212825 166803484,804596882,3882748894,18741593296,90476092366,436812623774,
%U A212825 2108996095916,10182801139146,49166003981046,237391983175872
%N A212825 Number of 0..4 arrays of length n with no adjacent pair equal to its immediately preceding adjacent pair, and new values introduced in 0..4 order.
%C A212825 Column 4 of A212829.
%H A212825 R. H. Hardin, <a href="/A212825/b212825.txt">Table of n, a(n) for n = 1..210</a>
%F A212825 Empirical: a(n) = 7*a(n-1) - 7*a(n-2) - 20*a(n-3) + 10*a(n-4) + 24*a(n-5) + 8*a(n-6) for n>9.
%F A212825 Empirical g.f.: x*(1 + x + x^2)*(1 - 6*x + 3*x^2 + 15*x^3 - 9*x^5 - 3*x^6) / ((1 - x - x^2)*(1 - 2*x - 2*x^2)*(1 - 4*x - 4*x^2)). - _Colin Barker_, Jul 21 2018
%e A212825 Some solutions for n=8:
%e A212825 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A212825 ..1....1....1....1....1....1....0....1....1....0....1....1....1....1....1....1
%e A212825 ..2....2....2....2....2....2....1....2....2....1....2....2....0....0....1....1
%e A212825 ..3....1....3....1....2....0....2....3....2....0....1....3....2....2....0....2
%e A212825 ..4....0....0....1....0....3....2....1....0....2....1....2....0....0....1....2
%e A212825 ..3....2....0....2....2....4....1....1....0....0....1....1....0....3....2....1
%e A212825 ..0....2....2....2....2....2....0....0....1....3....3....1....2....1....3....2
%e A212825 ..4....2....0....2....0....1....1....2....3....4....3....2....3....0....4....3
%Y A212825 Cf. A212829.
%K A212825 nonn
%O A212825 1,2
%A A212825 _R. H. Hardin_, May 28 2012