A220129 1 followed by period 12: (1, 5, 3, 9, 1, 7, 1, 9, 3, 5, 1, 11) repeated; offset 0.

1, 1, 5, 3, 9, 1, 7, 1, 9, 3, 5, 1, 11, 1, 5, 3, 9, 1, 7, 1, 9, 3, 5, 1, 11, 1, 5, 3, 9, 1, 7, 1, 9, 3, 5, 1, 11, 1, 5, 3, 9, 1, 7, 1, 9, 3, 5, 1, 11, 1, 5, 3, 9, 1, 7, 1, 9, 3, 5, 1, 11, 1, 5, 3, 9, 1, 7, 1, 9, 3, 5, 1, 11, 1, 5, 3, 9, 1, 7, 1, 9, 3, 5, 1, 11

Offset: 0

Author

Alois P. Heinz, Dec 06 2012

Keywords

• nonn
• easy
• changed

Comments

Also the number of tilings of an n X 4 rectangle using integer-sided rectangular tiles of area n.

Examples

			a(6) = 7, because there are 7 tilings of a 6 X 4 rectangle using integer-sided rectangular tiles of area 6:
._._._._.  ._._._._.  ._._____.  .___._._.
| | | | |  |     | |  | |     |  |   | | |
| | | | |  |_____| |  | |_____|  |   | | |
| | | | |  |     | |  | |     |  |___| | |
| | | | |  |_____| |  | |_____|  |   | | |
| | | | |  |     | |  | |     |  |   | | |
|_|_|_|_|  |_____|_|  |_|_____|  |___|_|_|
._.___._.  ._._.___.  .___.___.
| |   | |  | | |   |  |   |   |
| |   | |  | | |   |  |   |   |
| |___| |  | | |___|  |___|___|
| |   | |  | | |   |  |   |   |
| |   | |  | | |   |  |   |   |
|_|___|_|  |_|_|___|  |___|___|
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Row n=4 of A220122.

Programs

Maple

a:= n-> `if`(n=0, 1, [11, 1, 5, 3, 9, 1, 7, 1, 9, 3, 5, 1][irem(n, 12)+1]):
seq(a(n), n=0..100);

Mathematica

PadRight[{1},120,{11,1,5,3,9,1,7,1,9,3,5,1}] (* Harvey P. Dale, Aug 24 2025 *)

Formula

G.f.: -(10*x^6+11*x^5+16*x^4+9*x^3+7*x^2+2*x+1) / (x^6+x^5+x^4-x^2-x-1).