A193767 The number of dominoes in a largest saturated domino covering of the 4 by n board.

2, 5, 8, 12, 14, 17, 21, 24, 26, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135, 138, 141, 144, 147, 150, 153, 156, 159, 162, 165, 168, 171, 174, 177

Offset: 1

Author

Andrew Buchanan, Tanya Khovanova, Alex Ryba, Aug 06 2011

Keywords

• nonn
• easy

Comments

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

Examples

			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.
		

Links

• Andrew Buchanan, Tanya Khovanova and Alex Ryba, Saturated Domino Coverings, arXiv:1112.2115 [math.CO], 2011
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A193764, A193765, A193766, A193768.

Programs

Mathematica

LinearRecurrence[{2,-1},{2,5,8,12,14,17,21,24,26,30,33},60] (* Harvey P. Dale, Mar 25 2025 *)

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

Formula

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

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

a(n) = 2*a(n-1)-a(n-2) for n>11. - Colin Barker, Oct 05 2014

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