A220133 Number of tilings of an n X 8 rectangle using integer-sided rectangular tiles of area n.
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
Examples
a(5) = 5, because there are 5 tilings of a 5 X 8 rectangle using integer-sided rectangular tiles of area 5: ._._._._._._._._. ._________._._._. ._._________._._. | | | | | | | | | |_________| | | | | |_________| | | | | | | | | | | | |_________| | | | | |_________| | | | | | | | | | | | |_________| | | | | |_________| | | | | | | | | | | | |_________| | | | | |_________| | | |_|_|_|_|_|_|_|_| |_________|_|_|_| |_|_________|_|_| ._._._________._. ._._._._________. | | |_________| | | | | |_________| | | |_________| | | | | |_________| | | |_________| | | | | |_________| | | |_________| | | | | |_________| |_|_|_________|_| |_|_|_|_________|
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..1000
Crossrefs
Row n=8 of A220122.
Programs
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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);
Formula
G.f.: see Maple program.
Comments