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 A104519 Sufficient number of monominoes to exclude X-pentominoes from an n X n board. 5
 1, 2, 3, 4, 7, 10, 12, 16, 20, 24, 29, 35, 40, 47, 53, 60, 68, 76, 84, 92, 101, 111, 121, 131, 141, 152, 164, 176, 188, 200, 213, 227, 241, 255, 269, 284, 300, 316, 332, 348, 365, 383, 401, 419, 437, 456, 476, 496, 516 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,2 COMMENTS a(n+2) is also the domination number (size of minimal dominating set) in an n X n grid graph (Alanko et al.). Apparently also the minimal number of X-polyominoes needed to cover an n X n board. - Rob Pratt, Jan 03 2008 LINKS Samu Alanko, Simon Crevals, Anton Isopoussu, Patric R. J. Östergård and Ville Pettersson, Computing the Domination Number of Grid Graphs, The Electronic Journal of Combinatorics, 18 (2011), #P141. Eric Weisstein's World of Mathematics, Domination Number Eric Weisstein's World of Mathematics, Grid Graph FORMULA a(n) = n^2 - A193764(n). - Colin Barker, Oct 05 2014 Empirical g.f.: -x^3*(x^19 -2*x^18 +x^17 -x^14 +2*x^13 -3*x^12 +2*x^11 +x^10 -2*x^9 +2*x^7 -x^6 -x^5 +2*x^4 +1) / ((x -1)^3*(x^4 +x^3 +x^2 +x +1)) - Colin Barker, Oct 05 2014 Empirical recurrence a(n) = 2*a(n-1)-a(n-2)+a(n-5)-2*a(n-6)+a(n-7) with a(3)=-3, a(4)=-1, a(5)=1, a(6)=3, a(7)=5, a(8)=8, a(9)=12 matches the sequence for 9 <= n <= 14 and 16 <= n <= 51. - Eric W. Weisstein, Jun 27 2017 The first 51 terms can be described by the following collection of piecewise functions (written in Mathematica code): Table[Piecewise[{{n - 2, n <= 6}, {7, n == 7}, {10, n == 8}, {40, n == 15}}, Floor[n^2/5] - 4], {n, 3, 51}]. - Eric W. Weisstein, Apr 12 2016 CROSSREFS Cf. A193764, A269706 (size of a minimum dominating set in an n X n X n grid) Sequence in context: A204231 A135419 A051914 * A321684 A117220 A118426 Adjacent sequences:  A104516 A104517 A104518 * A104520 A104521 A104522 KEYWORD nonn AUTHOR Toshitaka Suzuki, Apr 19 2005 EXTENSIONS Extended to a(29) by Alanko et al. More terms from Colin Barker, Oct 05 2014 Keywords 'hard' and 'more' deleted by Colin Barker, Oct 05 2014 STATUS approved

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Last modified August 4 02:10 EDT 2020. Contains 336201 sequences. (Running on oeis4.)