A220130 Number of tilings of an n X 5 rectangle using integer-sided rectangular tiles of area n.

1, 1, 8, 4, 16, 2, 13, 1, 16, 4, 9, 1, 21, 1, 8, 5, 16, 1, 13, 1, 17, 4, 8, 1, 21, 2, 8, 4, 16, 1, 14, 1, 16, 4, 8, 2, 21, 1, 8, 4, 17, 1, 13, 1, 16, 5, 8, 1, 21, 1, 9, 4, 16, 1, 13, 2, 16, 4, 8, 1, 22, 1, 8, 4, 16, 2, 13, 1, 16, 4, 9, 1, 21, 1, 8, 5, 16, 1

Offset

0,3

Comments

1 followed by period 60: (1, 8, ..., 22) 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) = 4, because there are 4 tilings of a 3 X 5 rectangle using integer-sided rectangular tiles of area 3:
._._._._._.   ._____._._.   ._._____._.   ._._._____.
| | | | | |   |_____| | |   | |_____| |   | | |_____|
| | | | | |   |_____| | |   | |_____| |   | | |_____|
|_|_|_|_|_|   |_____|_|_|   |_|_____|_|   |_|_|_____|

Maple

gf:= -(21*x^12 +22*x^11 +51*x^10 +56*x^9 +80*x^8 +65*x^7 +72*x^6 +45*x^5 +40*x^4 +16*x^3 +11*x^2 +2*x +1) / (x^12 +x^11 +2*x^10 +2*x^9 +2*x^8 +x^7 -x^5 -2*x^4 -2*x^3 -2*x^2 -x -1):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..100);

Crossrefs

Row n=5 of A220122.

Sequence in context: A156279 A203072 A131873 * A276071 A040059 A178603

Adjacent sequences: A220127 A220128 A220129 * A220131 A220132 A220133

Keyword

nonn,easy

Author

Alois P. Heinz, Dec 06 2012

Status

approved