A226579 Smallest number of integer-sided squares needed to tile a 6 X n rectangle.

0, 6, 3, 2, 3, 5, 1, 5, 4, 3, 4, 6, 2, 6, 5, 4, 5, 7, 3, 7, 6, 5, 6, 8, 4, 8, 7, 6, 7, 9, 5, 9, 8, 7, 8, 10, 6, 10, 9, 8, 9, 11, 7, 11, 10, 9, 10, 12, 8, 12, 11, 10, 11, 13, 9, 13, 12, 11, 12, 14, 10, 14, 13, 12, 13, 15, 11, 15, 14, 13, 14, 16, 12, 16, 15, 14

Offset: 0

Author

Alois P. Heinz, Jun 12 2013

Keywords

• nonn
• easy

Examples

			a(13) = 6:
._._._._._._._._._._._._._.
|           |       |     |
|           |       |     |
|           |       |_____|
|           |_______|     |
|           |   |   |     |
|___________|___|___|_____|
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,1,1,0,-1)

Crossrefs

Row m=6 of A113881, A219158.

Programs

Maple

a:= n-> `if`(n=1, 6, iquo(n, 6, 'r') +[0, 4, 3, 2, 3, 5][r+1]):
seq(a(n), n=0..100);

Mathematica

Join[{0,6},LinearRecurrence[{0,1,1,0,-1},{3,2,3,5,1},80]] (* Harvey P. Dale, Jun 03 2014 *)

Formula

G.f.: x*(2*x^5-6*x^3-4*x^2+3*x+6)/(x^5-x^3-x^2+1).

a(n) = 1 + a(n-6) for n>7.