This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A193767 #19 Mar 25 2025 16:24:43
%S A193767 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 A193767 75,78,81,84,87,90,93,96,99,102,105,108,111,114,117,120,123,126,129,
%U A193767 132,135,138,141,144,147,150,153,156,159,162,165,168,171,174,177
%N A193767 The number of dominoes in a largest saturated domino covering of the 4 by n board.
%C A193767 A domino covering of a board is saturated if the removal of any domino leaves an uncovered cell.
%H A193767 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 A193767 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A193767 a(n) = 3n, except for n = 1, 2, 3, 5, 6 or 9. For the exceptions a(n) = 3n-1.
%F A193767 a(n) = 4n - A193768(n).
%F A193767 a(n) = 2*a(n-1)-a(n-2) for n>11. - _Colin Barker_, Oct 05 2014
%F A193767 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 A193767 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.
%t A193767 LinearRecurrence[{2,-1},{2,5,8,12,14,17,21,24,26,30,33},60] (* _Harvey P. Dale_, Mar 25 2025 *)
%o A193767 (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 A193767 Cf. A193764, A193765, A193766, A193768.
%K A193767 nonn,easy
%O A193767 1,1
%A A193767 Andrew Buchanan, _Tanya Khovanova_, Alex Ryba, Aug 06 2011