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Number of length n+2 0..4 arrays with no pair in any consecutive three terms totalling exactly 4.
1

%I #10 Nov 05 2018 21:03:11

%S 64,208,676,2196,7132,23168,75260,244464,794096,2579500,8379052,

%T 27217860,88412560,287192948,932896352,3030352272,9843575108,

%U 31975148500,103865731612,337389844512,1095952482460,3560011839440,11564081956784

%N Number of length n+2 0..4 arrays with no pair in any consecutive three terms totalling exactly 4.

%H R. H. Hardin, <a href="/A245991/b245991.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + a(n-2) + 9*a(n-3) + 3*a(n-4).

%F Empirical g.f.: 4*x*(16 + 20*x + 49*x^2 + 15*x^3) / (1 - 2*x - x^2 - 9*x^3 - 3*x^4). - _Colin Barker_, Nov 05 2018

%e Some solutions for n=7:

%e 3 3 4 0 2 2 3 2 2 3 4 3 4 0 4 0

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

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

%e 4 2 2 2 0 4 4 3 2 3 3 0 0 3 4 2

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

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

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

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

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

%Y Column 4 of A245995.

%K nonn

%O 1,1

%A _R. H. Hardin_, Aug 09 2014