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A193767
The number of dominoes in a largest saturated domino covering of the 4 by n board.
4
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
1,1
COMMENTS
A domino covering of a board is saturated if the removal of any domino leaves an uncovered cell.
LINKS
Andrew Buchanan, Tanya Khovanova and Alex Ryba, Saturated Domino Coverings, arXiv:1112.2115 [math.CO], 2011
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
EXAMPLE
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.
PROG
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Andrew Buchanan, Tanya Khovanova, Alex Ryba, Aug 06 2011
STATUS
approved