A220132 Number of tilings of an n X 7 rectangle using integer-sided rectangular tiles of area n.

1, 1, 21, 9, 65, 4, 88, 2, 65, 9, 26, 1, 180, 1, 22, 12, 65, 1, 88, 1, 70, 10, 21, 1, 180, 4, 21, 9, 66, 1, 93, 1, 65, 9, 21, 5, 180, 1, 21, 9, 70, 1, 89, 1, 65, 12, 21, 1, 180, 2, 26, 9, 65, 1, 88, 4, 66, 9, 21, 1, 185, 1, 21, 10, 65, 4, 88, 1, 65, 9, 27, 1

Offset

0,3

Comments

1 followed by period 420: (1, 21, ..., 186) repeated; offset 0.

Links

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

Formula

G.f.: see Maple program.

Example

a(5) = 4, because there are 4 tilings of a 5 X 7 rectangle using integer-sided rectangular tiles of area 5:
._._._._._._._.  ._________._._.
| | | | | | | |  |_________| | |
| | | | | | | |  |_________| | |
| | | | | | | |  |_________| | |
| | | | | | | |  |_________| | |
|_|_|_|_|_|_|_|  |_________|_|_|
._._________._.  ._._._________.
| |_________| |  | | |_________|
| |_________| |  | | |_________|
| |_________| |  | | |_________|
| |_________| |  | | |_________|
|_|_________|_|  |_|_|_________|

Maple

gf:= -(185*x^26 +186*x^25 +392*x^24 +402*x^23 +673*x^22 +687*x^21 +1046*x^20 +877*x^19 +1300*x^18 +1119*x^17 +1374*x^16 +1128*x^15 +1353*x^14 +1010*x^13 +1169*x^12 +760*x^11 +822*x^10 +567*x^9 +564*x^8 +325*x^7 +310*x^6 +135*x^5 +121*x^4 +34*x^3 +24*x^2 +2*x +1) /
(x^26 +x^25 +2*x^24 +2*x^23 +3*x^22 +3*x^21 +4*x^20 +3*x^19 +4*x^18 +3*x^17 +3*x^16 +2*x^15 +x^14 -x^12 -2*x^11 -3*x^10 -3*x^9 -4*x^8 -3*x^7 -4*x^6 -3*x^5 -3*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=7 of A220122.

Sequence in context: A040425 A337422 A040424 * A146375 A371096 A040423

Adjacent sequences: A220129 A220130 A220131 * A220133 A220134 A220135

Keyword

nonn,easy

Author

Alois P. Heinz, Dec 06 2012

Status

approved