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A202117 Number of -1..1 arrays of n elements with first, second and third differences also in -1..1.

%I A202117 #10 May 27 2018 06:56:14
%S A202117 3,7,13,19,27,35,47,65,91,129,185,267,387,563,821,1199,1753,2565,3755,
%T A202117 5499,8055,11801,17291,25337,37129,54411,79739,116859,171261,250991,
%U A202117 367841,539093,790075,1157907,1696991,2487057,3644955,5341937,7828985
%N A202117 Number of -1..1 arrays of n elements with first, second and third differences also in -1..1.
%C A202117 Column 1 of A202124.
%H A202117 R. H. Hardin, <a href="/A202117/b202117.txt">Table of n, a(n) for n = 1..210</a>
%F A202117 Empirical: a(n) = 2*a(n-1) -a(n-2) +a(n-3) -a(n-4) for n>8.
%F A202117 Empirical g.f.: x*(3 + x + 2*x^2 - 3*x^3 - 2*x^4 - 6*x^5 - 2*x^6 - 2*x^7) / ((1 - x)*(1 - x - x^3)). - _Colin Barker_, May 27 2018
%e A202117 Some solutions for n=7:
%e A202117 ..1....1....1....0....1....1....0....0....1....1...-1...-1...-1....1...-1....0
%e A202117 ..1....0....1...-1....0....1...-1....1....1....1....0...-1...-1....0....0....0
%e A202117 ..1...-1....1...-1....0....0...-1....1....1....1....0...-1....0....0....1....0
%e A202117 ..1...-1....1....0....0...-1...-1....1....1....0....0...-1....1....0....1....0
%e A202117 ..1....0....1....1....0...-1...-1....0....0...-1....0...-1....1....0....1....0
%e A202117 ..1....1....1....1....0....0....0...-1...-1...-1....0...-1....0....0....1....0
%e A202117 ..0....1....1....0...-1....1....1...-1...-1...-1....1...-1...-1....0....0....0
%Y A202117 Cf. A202124.
%K A202117 nonn
%O A202117 1,1
%A A202117 _R. H. Hardin_, Dec 11 2011