A220131 Number of tilings of an n X 6 rectangle using integer-sided rectangular tiles of area n.

1, 1, 13, 6, 35, 3, 46, 1, 35, 6, 15, 1, 88, 1, 13, 8, 35, 1, 46, 1, 37, 6, 13, 1, 88, 3, 13, 6, 35, 1, 48, 1, 35, 6, 13, 3, 88, 1, 13, 6, 37, 1, 46, 1, 35, 8, 13, 1, 88, 1, 15, 6, 35, 1, 46, 3, 35, 6, 13, 1, 90, 1, 13, 6, 35, 3, 46, 1, 35, 6, 15, 1, 88, 1, 13

Offset

0,3

Comments

1 followed by period 60: (1, 13, ..., 90) repeated; offset 0.

Links

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

Formula

G.f.: see Maple program.

Example

a(3) = 6, because there are 6 tilings of a 3 X 6 rectangle using integer-sided rectangular tiles of area 3:
._._._._._._.   ._____._._._.   ._._____._._.
| | | | | | |   |_____| | | |   | |_____| | |
| | | | | | |   |_____| | | |   | |_____| | |
|_|_|_|_|_|_|   |_____|_|_|_|   |_|_____|_|_|
._._._____._.   ._._._._____.   ._____._____.
| | |_____| |   | | | |_____|   |_____|_____|
| | |_____| |   | | | |_____|   |_____|_____|
|_|_|_____|_|   |_|_|_|_____|   |_____|_____|

Maple

gf:= -(89*x^16 +90*x^15 +103*x^14 +109*x^13 +144*x^12 +58*x^11 +103*x^10 +91*x^9 +120*x^8 +91*x^7 +103*x^6 +58*x^5 +56*x^4 +21*x^3 +15*x^2 +2*x +1) / (x^16 +x^15 +x^14 +x^13 +x^12 -x^4 -x^3 -x^2 -x -1):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..100);

Crossrefs

Row n=6 of A220122.

Sequence in context: A300504 A168210 A206612 * A268723 A300942 A160247

Adjacent sequences: A220128 A220129 A220130 * A220132 A220133 A220134

Keyword

nonn,easy

Author

Alois P. Heinz, Dec 06 2012

Status

approved