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A220133
Number of tilings of an n X 8 rectangle using integer-sided rectangular tiles of area n.
2
1, 1, 34, 13, 143, 5, 209, 3, 250, 13, 44, 1, 472, 1, 36, 19, 250, 1, 209, 1, 153, 15, 34, 1, 681, 5, 34, 13, 145, 1, 221, 1, 250, 13, 34, 7, 472, 1, 34, 13, 260, 1, 211, 1, 143, 19, 34, 1, 681, 3, 44, 13, 143, 1, 209, 5, 252, 13, 34, 1, 484, 1, 34, 15, 250, 5
OFFSET
0,3
COMMENTS
1 followed by period 840: (1, 34, ..., 695) repeated; offset 0.
LINKS
FORMULA
G.f.: see Maple program.
EXAMPLE
a(5) = 5, because there are 5 tilings of a 5 X 8 rectangle using integer-sided rectangular tiles of area 5:
._._._._._._._._. ._________._._._. ._._________._._.
| | | | | | | | | |_________| | | | | |_________| | |
| | | | | | | | | |_________| | | | | |_________| | |
| | | | | | | | | |_________| | | | | |_________| | |
| | | | | | | | | |_________| | | | | |_________| | |
|_|_|_|_|_|_|_|_| |_________|_|_|_| |_|_________|_|_|
._._._________._. ._._._._________.
| | |_________| | | | | |_________|
| | |_________| | | | | |_________|
| | |_________| | | | | |_________|
| | |_________| | | | | |_________|
|_|_|_________|_| |_|_|_|_________|
MAPLE
gf:= -(694*x^46 +x^45 +728*x^44 +708*x^43 +872*x^42 +1441*x^41 +1789*x^40 +928*x^39 +2784*x^38 +1967*x^37 +2307*x^36 +3029*x^35 +3122*x^34 +2593*x^33 +4196*x^32 +2514*x^31 +3854*x^30 +3978*x^29 +3762*x^28
+3055*x^27 +4448*x^26 +2969*x^25 +4154*x^24 +3352*x^23 +3461*x^22 +2969*x^21 +3755*x^20 +2362*x^19 +3069*x^18 +2592*x^17 +2468*x^16 +1821*x^15 +2117*x^14 +1207*x^13 +1736*x^12 +950*x^11 +921*x^10 +581*x^9 +705*x^8 +235*x^7 +403*x^6 +55*x^5 +179*x^4 +15*x^3 +35*x^2 +x +1) /
(x^46 +x^44 +x^43 +x^42 +2*x^41 +2*x^40 +x^39 +3*x^38 +2*x^37 +2*x^36 +3*x^35 +2*x^34 +2*x^33 +3*x^32 +x^31 +2*x^30 +2*x^29 +x^28 +x^27 +x^26
+x^24 -x^22 -x^20 -x^19 -x^18 -2*x^17 -2*x^16 -x^15 -3*x^14 -2*x^13 -2*x^12 -3*x^11 -2*x^10 -2*x^9 -3*x^8 -x^7 -2*x^6 -2*x^5 -x^4 -x^3 -x^2 -1):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..80);
CROSSREFS
Row n=8 of A220122.
Sequence in context: A350132 A350934 A071788 * A300101 A298258 A298929
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Dec 06 2012
STATUS
approved