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%I A193764 #22 Jan 25 2024 11:44:20
%S A193764 2,6,12,18,26,37,48,61,76,92,109,129,149,172,196,221,248,277,308,340,
%T A193764 373,408,445,484,524,565,608,653,700,748,797,848,901,956,1012,1069,
%U A193764 1128,1189,1252,1316,1381,1448,1517,1588,1660,1733,1808,1885,1964,2044,2125
%N A193764 The number of dominoes in a largest saturated domino covering of the n X n board (n>=2).
%C A193764 A domino covering of a board is saturated if the removal of any domino leaves an uncovered cell.
%H A193764 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 A193764 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (2, -1, 0, 0, 1, -2, 1).
%F A193764 For n > 6, except n = 13, a(n) = n^2 + 4 - floor((n+2)^2/5).
%F A193764 a(n) = n^2 - A104519(n).
%F A193764 Empirical g.f.: x^2*(x^18 -2*x^17 +x^16 -x^13 +2*x^12 -3*x^11 +2*x^10 +x^9 -2*x^8 +2*x^6 -x^5 -2*x^4 -2*x^2 -2*x -2) / ((x -1)^3*(x^4 +x^3 +x^2 +x +1)). - _Colin Barker_, Oct 05 2014
%F A193764 Empirical g.f. confirmed with above formula and recurrence in A104519. - _Ray Chandler_, Jan 25 2024
%e A193764 If you completely cover a 2 X 2 board with 3 dominoes, you can remove one and the board will still be covered. Hence a(2) < 3. On the other hand, you can tile the 2 X 2 board with 2 dominoes and a removal of one of them will leave both cells uncovered. Hence a(2) = 2.
%Y A193764 Cf. A104519, A193765, A193766, A193767, A193768.
%K A193764 nonn
%O A193764 2,1
%A A193764 Andrew Buchanan, _Tanya Khovanova_, Alex Ryba, Aug 06 2011

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