A193703 - OEIS

%I #13 May 04 2018 22:41:22

%S 1,3,9,27,73,195,515,1357,3585,9479,25069,66307,175381,463859,1226827,

%T 3244745,8581777,22697291,60030393,158769987,419919089,1110613203,

%U 2937379387,7768859149,20547285345,54344006943,143730475357,380142185163

%N Number of arrays of -1..1 integers x(1..n) with every x(i) in a subsequence of length 1, 2, 3 or 4 with sum zero.

%C Column 1 of A193710.

%H R. H. Hardin, <a href="/A193703/b193703.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 2*a(n-1) +a(n-2) +2*a(n-3) -a(n-4) +3*a(n-6) +4*a(n-7).

%F Empirical g.f.: x*(1 + x)^2*(1 - x + 3*x^2 - x^3 + 4*x^4) / (1 - 2*x - x^2 - 2*x^3 + x^4 - 3*x^6 - 4*x^7). - _Colin Barker_, May 04 2018

%e Some solutions for n=6:

%e    1  0  1  0 -1 -1  0  0  1  0 -1 -1  0 -1  1  0

%e   -1 -1 -1  1  1  1  1  0 -1  0  0  1  0  1 -1 -1

%e    0  1 -1  0  1  1 -1 -1  0  0  1  1  1  0  0  1

%e    1  1  1 -1  0 -1 -1  1  0 -1 -1 -1 -1  1 -1  0

%e    0 -1  1  0  0  0  1 -1  0  1  0  1  1  0  0  1

%e    0  1  0  0 -1  0 -1  0  0  0  0 -1 -1 -1  1 -1

%Y Cf. A193710.

%K nonn

%O 1,2

%A _R. H. Hardin_, Aug 02 2011