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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

Table of n, a(n) for n=3..51.

Samu Alanko, Simon Crevals, Anton Isopoussu, Patric Ostergard 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 June 25 22:16 EDT 2019. Contains 324358 sequences. (Running on oeis4.)