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A212826 Number of 0..5 arrays of length n with no adjacent pair equal to its immediately preceding adjacent pair, and new values introduced in 0..5 order.

%I A212826 #10 Jul 21 2018 10:06:57
%S A212826 1,2,5,13,44,168,716,3331,16599,87059,473569,2641428,14982656,
%T A212826 85930423,496412949,2881216925,16773626497,97843056510,571457023718,
%U A212826 3340356838651,19535838889479,114293073644447,668811749036809,3914263576403496
%N A212826 Number of 0..5 arrays of length n with no adjacent pair equal to its immediately preceding adjacent pair, and new values introduced in 0..5 order.
%C A212826 Column 5 of A212829.
%H A212826 R. H. Hardin, <a href="/A212826/b212826.txt">Table of n, a(n) for n = 1..210</a>
%F A212826 Empirical: a(n) = 11*a(n-1) - 30*a(n-2) - 21*a(n-3) + 112*a(n-4) + 63*a(n-5) - 119*a(n-6) - 120*a(n-7) - 30*a(n-8) for n>11.
%F A212826 Empirical g.f.: x*(1 + x + x^2)*(1 - 10*x + 22*x^2 + 27*x^3 - 68*x^4 - 67*x^5 + 29*x^6 + 44*x^7 + 11*x^8) / ((1 - x - x^2)*(1 - 2*x - 2*x^2)*(1 - 3*x - 3*x^2)*(1 - 5*x - 5*x^2)). - _Colin Barker_, Jul 21 2018
%e A212826 Some solutions for n=8:
%e A212826 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A212826 ..0....1....1....1....0....1....1....1....1....1....1....1....1....1....1....1
%e A212826 ..1....2....1....2....0....1....1....2....0....1....2....2....0....1....2....1
%e A212826 ..0....3....2....0....1....2....2....3....2....2....1....3....2....2....3....0
%e A212826 ..2....3....3....0....0....3....3....0....1....1....0....2....2....3....4....2
%e A212826 ..3....4....1....0....2....4....2....2....1....0....3....1....2....4....5....3
%e A212826 ..1....3....2....1....2....2....4....3....3....0....2....0....3....3....4....2
%e A212826 ..1....3....3....1....3....4....3....3....1....2....1....2....1....5....4....0
%Y A212826 Cf. A212829.
%K A212826 nonn
%O A212826 1,2
%A A212826 _R. H. Hardin_, May 28 2012