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%I #10 Jul 22 2018 06:42:20
%S 4,17,257,3074,40434,522515,6800539,88363628,1148860844,14934544493,
%T 194151313701,2523957115862,32811479230534,426549073848551,
%U 5545138556625743,72086798766250976,937128393589298304
%N Number of 0..4 colorings of a 2 X (n+1) array circular in the n+1 direction with new values 0..4 introduced in row major order.
%C Row 2 of A214141.
%H R. H. Hardin, <a href="/A214143/b214143.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 10*a(n-1) + 50*a(n-2) - 116*a(n-3) - 361*a(n-4) + 106*a(n-5) + 312*a(n-6).
%F Empirical: 3^n/4 +13^(n+1)/120 -(-1)^n/6 +(-2)^(n+1)/5 -2*(-4)^n/15 +41/120. - _R. J. Mathar_, Jul 07 2012
%F Empirical g.f.: x*(4 - 23*x - 113*x^2 + 118*x^3 + 260*x^4) / ((1 - x)*(1 + x)*(1 + 2*x)*(1 - 3*x)*(1 + 4*x)*(1 - 13*x)). - _Colin Barker_, Jul 22 2018
%e Some solutions for n=4:
%e ..0..1..2..3..1....0..1..0..1..2....0..1..2..3..2....0..1..2..3..2
%e ..3..4..3..1..2....1..0..1..2..3....1..2..3..0..3....1..4..3..1..0
%Y Cf. A214141.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jul 05 2012
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