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
Index entries for linear recurrences with constant coefficients, signature (2,-1).
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