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

0,3

Comments

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

Links

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

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).

Example

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

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);

Crossrefs

Row n=4 of A220122.

Sequence in context: A092748 A078302 A199438 * A192039 A305327 A112812

Adjacent sequences: A220126 A220127 A220128 * A220130 A220131 A220132

Keyword

nonn,easy

Author

Alois P. Heinz, Dec 06 2012

Status

approved