A193766 The number of dominoes in a largest saturated domino covering of the 3 by n board.

2, 4, 6, 8, 11, 13, 15, 17, 20, 22, 24, 26, 29, 31, 33, 35, 38, 40, 42, 44, 47, 49, 51, 53, 56, 58, 60, 62, 65, 67, 69, 71, 74, 76, 78, 80, 83, 85, 87, 89, 92, 94, 96, 98, 101, 103, 105, 107, 110, 112, 114, 116, 119, 121, 123, 125, 128, 130, 132, 134, 137

Offset

1,1

Comments

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

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 (1,0,0,1,-1)

Formula

a(n) = 3*n - floor((3*n+4)/4) = 3*n - A077915(n).

G.f. x*(2+2*x+2*x^2+2*x^3+x^4) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Aug 22 2011

Example

If you completely cover a 3 by 1 board with 3 dominoes, you can always remove one and the board will still be covered. Hence a(2) < 3. On the other hand, you can cover the 2 by 2 board with 2 dominoes and a removal of one of them will leave one cell uncovered. Hence a(1) = 2.

Mathematica

Table[3 n - Floor[(3 n + 4)/4], {n, 100}]
LinearRecurrence[{1, 0, 0, 1, -1}, {2, 4, 6, 8, 11}, 70] (* Harvey P. Dale, Dec 11 2015 *)

Prog

(PARI) a(n) = 3*n - (3*n+4)\4 \\ Charles R Greathouse IV, Jun 11 2015

Crossrefs

Cf. A077915, A193764, A193765, A193767, A193768.

Sequence in context: A241176 A184809 A022839 * A262773 A186152 A004401

Adjacent sequences: A193763 A193764 A193765 * A193767 A193768 A193769

Keyword

nonn,easy

Author

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

Status

approved