A193645 - OEIS

A193645

Number of arrays of -5..5 integers x(1..n) with every x(i) in a subsequence of length 1 or 2 with sum zero.

%I #11 May 04 2018 22:41:15

%S 1,11,31,151,561,2361,9361,38171,153591,621911,2510721,10150321,

%T 41008321,165729931,669676751,2706201271,10935546481,44190379881,

%U 178571332881,721601251291,2915963545511,11783308434231,47615926483841

%N Number of arrays of -5..5 integers x(1..n) with every x(i) in a subsequence of length 1 or 2 with sum zero.

%C Column 5 of A193648.

%H R. H. Hardin, <a href="/A193645/b193645.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 2*a(n-1) +8*a(n-2) +a(n-3).

%F Empirical g.f.: x*(1 + 9*x + x^2) / (1 - 2*x - 8*x^2 - x^3). - _Colin Barker_, May 04 2018

%e Some solutions for n=6:

%e -5 -5 0 4 -5 5 4 0 -4 -5 0 0 0 2 1 1

%e 5 5 3 -4 5 -5 -4 5 4 5 0 -2 2 -2 -1 -1

%e 2 -1 -3 4 5 -3 1 -5 -4 -5 -2 2 -2 5 1 3

%e -2 1 -4 1 -5 3 -1 5 1 5 2 -2 0 -5 -3 -3

%e -3 5 4 -1 4 0 -1 -2 -1 -4 3 -3 0 1 3 -1

%e 3 -5 0 1 -4 0 1 2 0 4 -3 3 0 -1 -3 1

%Y Cf. A193648.

%K nonn

%O 1,2

%A _R. H. Hardin_, Aug 02 2011