A193697 - OEIS

%I #5 Mar 31 2012 12:36:21

%S 1,7,43,181,827,3773,17197,78407,357403,1629369,7428007,33862711,

%T 154372795,703751937,3208252657,14625730979,66675552791,303959466209,

%U 1385685646663,6317041957501,28798031581467,131284013681727

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

%C Column 3 of A193702

%H R. H. Hardin, <a href="/A193697/b193697.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 4*a(n-1) +a(n-2) -a(n-3) +21*a(n-4) +47*a(n-5) +60*a(n-6) +155*a(n-7) +255*a(n-8) +386*a(n-9) +623*a(n-10) +899*a(n-11) +976*a(n-12) +972*a(n-13) +664*a(n-14) +119*a(n-15) -414*a(n-16) -754*a(n-17) -970*a(n-18) -886*a(n-19) -786*a(n-20) -580*a(n-21) -358*a(n-22) -109*a(n-23) +40*a(n-24) +116*a(n-25) +100*a(n-26) +66*a(n-27) +37*a(n-28) +19*a(n-29) +6*a(n-30) +a(n-31)

%e Some solutions for n=6

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

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

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

%e ..1...-3...-3....1....2...-2....1....1...-1...-2...-2...-1...-3....1...-2....1

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

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

%K nonn

%O 1,2

%A _R. H. Hardin_ Aug 02 2011