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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. 1

%I

%S 1,2,5,13,44,168,716,3331,16599,87059,473569,2641428,14982656,

%T 85930423,496412949,2881216925,16773626497,97843056510,571457023718,

%U 3340356838651,19535838889479,114293073644447,668811749036809,3914263576403496

%N 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 Column 5 of A212829.

%H R. H. Hardin, <a href="/A212826/b212826.txt">Table of n, a(n) for n = 1..210</a>

%F 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 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 Some solutions for n=8:

%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

%e ..0....1....1....1....0....1....1....1....1....1....1....1....1....1....1....1

%e ..1....2....1....2....0....1....1....2....0....1....2....2....0....1....2....1

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

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

%e ..3....4....1....0....2....4....2....2....1....0....3....1....2....4....5....3

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

%e ..1....3....3....1....3....4....3....3....1....2....1....2....1....5....4....0

%Y Cf. A212829.

%K nonn

%O 1,2

%A _R. H. Hardin_, May 28 2012

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Last modified December 5 06:15 EST 2022. Contains 358578 sequences. (Running on oeis4.)