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Half the number of 0..3 arrays of length n+2 with second differences nonzero.
1

%I #8 Jul 21 2018 10:06:01

%S 28,99,350,1238,4379,15490,54793,193821,685609,2425226,8578828,

%T 30346157,107344412,379712753,1343169821,4751236703,16806698494,

%U 59450861306,210297394895,743891565706,2631390949017,9308101672049,32925839761497

%N Half the number of 0..3 arrays of length n+2 with second differences nonzero.

%C Column 3 of A212782.

%H R. H. Hardin, <a href="/A212777/b212777.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + 5*a(n-2) + 3*a(n-3) - 4*a(n-4) - 4*a(n-5).

%F Empirical g.f.: x*(28 + 43*x + 12*x^2 - 41*x^3 - 32*x^4) / (1 - 2*x - 5*x^2 - 3*x^3 + 4*x^4 + 4*x^5). - _Colin Barker_, Jul 21 2018

%e Some solutions for n=5:

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

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

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

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

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

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

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

%Y Cf. A212782.

%K nonn

%O 1,1

%A _R. H. Hardin_, May 27 2012