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A220132 Number of tilings of an n X 7 rectangle using integer-sided rectangular tiles of area n. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
1 followed by period 420: (1, 21, ..., 186) repeated; offset 0.
LINKS
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 A040423 A318648
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Dec 06 2012
STATUS
approved

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Last modified February 26 04:47 EST 2024. Contains 370335 sequences. (Running on oeis4.)