The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #16 Jun 19 2024 07:40:40
%S 1,2,4,11,25,61,146,351,844,2028,4875,11717,28163,67692,162703,391070,
%T 939968,2259289,5430383,13052363,31372406,75406105,181244648,
%U 435636112,1047086489,2516756727,6049227537,14539805696,34947594281,83999358146,201899224084,485281049587,1166412095721
%N Number of placements of zero or more dominoes on a 2 X n grid where no two empty squares are horizontally adjacent.
%H Andrew Howroyd, <a href="/A329707/b329707.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,0,0,0,-1).
%F a(n) = 2*a(n-1) + a(n-2) - a(n-6) for n > 6.
%F G.f.: (1 - x)*(1 + x + x^3)/(1 - 2*x - x^2 + x^6).
%t LinearRecurrence[{2, 1, 0, 0, 0, -1}, {1, 2, 4, 11, 25, 61}, 50] (* _Paolo Xausa_, Jun 19 2024 *)
%o (PARI) Vec((1 - x)*(1 + x + x^3)/(1 - 2*x - x^2 + x^6) + O(x^30))
%Y Row 2 of A332862.
%K nonn
%O 0,2
%A _Andrew Howroyd_, Feb 28 2020