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

%I #7 Jul 01 2013 13:24:12

%S 11,27,66,162,397,973,2385,5846,14329,35122,86088,211011,517211,

%T 1267741,3107372,7616509,18668898,45759514,112161581,274920321,

%U 673859821,1651704234,4048508001,9923336574,24323184920,59618790539,146132186103

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

%C Column 2 of A212782

%H R. H. Hardin, <a href="/A212776/b212776.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical: G.f. -x*(11+16*x+17*x^2+9*x^3) / ( -1+x+2*x^2+3*x^3+2*x^4 ). - _R. J. Mathar_, Jul 01 2013

%e Some solutions for n=5

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

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

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ May 27 2012