%I #17 Jun 13 2015 00:53:56

%S 2,5,8,12,14,17,21,24,26,30,33,36,39,42,45,48,51,54,57,60,63,66,69,72,

%T 75,78,81,84,87,90,93,96,99,102,105,108,111,114,117,120,123,126,129,

%U 132,135,138,141,144,147,150,153,156,159,162,165,168,171,174,177

%N The number of dominoes in a largest saturated domino covering of the 4 by n board.

%C A domino covering of a board is saturated if the removal of any domino leaves an uncovered cell.

%H Andrew Buchanan, Tanya Khovanova and Alex Ryba, <a href="http://arxiv.org/abs/1112.2115">Saturated Domino Coverings</a>, arXiv:1112.2115 [math.CO], 2011

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F a(n) = 3n, except for n = 1, 2, 3, 5, 6 or 9. For the exceptions a(n) = 3n-1.

%F a(n) = 4n - A193768(n).

%F a(n) = 2*a(n-1)-a(n-2) for n>11. - _Colin Barker_, Oct 05 2014

%F G.f.: -x*(x^10-2*x^9+x^8+x^7-x^6-x^5+2*x^4-x^3-x-2) / (x-1)^2. - _Colin Barker_, Oct 05 2014

%e You have to have at least two dominoes to cover the 1 by 4 board, each covering the corner. After that anything else you can remove. Hence a(1) = 2.

%o (PARI) Vec(-x*(x^10-2*x^9+x^8+x^7-x^6-x^5+2*x^4-x^3-x-2)/(x-1)^2 + O(x^100)) \\ _Colin Barker_, Oct 05 2014

%Y Cf. A193764, A193765, A193766, A193768.

%K nonn,easy

%O 1,1

%A Andrew Buchanan, _Tanya Khovanova_, Alex Ryba, Aug 06 2011