cp's OEIS Frontend

A193697 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.

%I A193697 #10 Apr 27 2025 09:08:15
%S A193697 1,7,43,181,827,3773,17197,78407,357403,1629369,7428007,33862711,
%T A193697 154372795,703751937,3208252657,14625730979,66675552791,303959466209,
%U A193697 1385685646663,6317041957501,28798031581467,131284013681727,598495497977845,2728411869163663,12438241145358561
%N A193697 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.
%H A193697 R. H. Hardin, <a href="/A193697/b193697.txt">Table of n, a(n) for n = 1..200</a>
%F A193697 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 A193697 Some solutions for n=6:
%e A193697 ..3...-2....0....2...-3....1....1...-2....2...-3...-3...-2....0...-3....3....3
%e A193697 .-3....0....0...-1....2...-3....1....2....0....1....0....2....1....0...-3...-3
%e A193697 ..2....2....0...-1....1....2...-2....0...-2....2....3....0....2....3....2...-1
%e A193697 ..1...-3...-3....1....2...-2....1....1...-1...-2...-2...-1...-3....1...-2....1
%e A193697 ..1....1....3...-1...-3....2....1...-3....2....0....0....1....2...-2...-1....2
%e A193697 .-2...-1...-3....0....1....0...-2....2...-1....0....2...-1....1....1....3...-2
%Y A193697 Column 3 of A193702.
%K A193697 nonn
%O A193697 1,2
%A A193697 _R. H. Hardin_, Aug 02 2011