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A220135
Number of tilings of an n X 10 rectangle using integer-sided rectangular tiles of area n.
2
1, 1, 89, 28, 590, 8, 1002, 5, 1209, 64, 254, 1, 2861, 1, 99, 47, 1209, 1, 1274, 1, 1045, 34, 89, 1, 4146, 8, 89, 64, 600, 1, 1527, 1, 1209, 28, 89, 12, 3197, 1, 89, 28, 1968, 1, 1014, 1, 590, 83, 89, 1, 4146, 5, 254, 28, 590, 1, 1274, 8, 1219, 28, 89, 1, 3904
OFFSET
0,3
COMMENTS
1 followed by period 2520: (1, 89, ..., 5841) repeated; offset 0.
LINKS
FORMULA
G.f.: see Maple program.
EXAMPLE
a(7) = 5, because there are 5 tilings of a 7 X 10 rectangle using integer-sided rectangular tiles of area 7:
._._._._._._._._._._. ._____________._._._. ._._____________._._.
| | | | | | | | | | | |_____________| | | | | |_____________| | |
| | | | | | | | | | | |_____________| | | | | |_____________| | |
| | | | | | | | | | | |_____________| | | | | |_____________| | |
| | | | | | | | | | | |_____________| | | | | |_____________| | |
| | | | | | | | | | | |_____________| | | | | |_____________| | |
| | | | | | | | | | | |_____________| | | | | |_____________| | |
|_|_|_|_|_|_|_|_|_|_| |_____________|_|_|_| |_|_____________|_|_|
._._._____________._. ._._._._____________.
| | |_____________| | | | | |_____________|
| | |_____________| | | | | |_____________|
| | |_____________| | | | | |_____________|
| | |_____________| | | | | |_____________|
| | |_____________| | | | | |_____________|
| | |_____________| | | | | |_____________|
|_|_|_____________|_| |_|_|_|_____________|
MAPLE
gf:= -(-5840*x^136 +5839*x^135 -5928*x^134 +60*x^133 +5189*x^132 -5285*x^131 -1496*x^130 +928*x^129 -7484*x^128 +557*x^127 -494*x^126 -836*x^125 -14180*x^124 +13384*x^123 -15627*x^122 -5927*x^121 +10767*x^120 -12422*x^119 -11498*x^118 +8324*x^117 -24921*x^116 +5813*x^115 -7409*x^114 -3505*x^113 -22788*x^112 +13672*x^111 -27634*x^110 -12862*x^109 +11206*x^108 -17207*x^107 -26452*x^106
+17129*x^105 -50277*x^104 +11512*x^103 -17938*x^102 -12787*x^101 -23042*x^100 +7805*x^99 -45002*x^98 -10518*x^97 -2969*x^96 -17338*x^95 -39604*x^94 +21144*x^93 -68673*x^92 +12881*x^91 -28074*x^90 -22885*x^89 -22229*x^88 +3198*x^87 -63456*x^86 +9*x^85 -20501*x^84 -17035*x^83 -44066*x^82 +17258*x^81 -76763*x^80 +11371*x^79 -35515*x^78 -26786*x^77 -19392*x^76 +967*x^75 -73127*x^74 +8938*x^73 -34070*x^72 -17281*x^71
-40042*x^70 +11259*x^69 -71956*x^68 +11259*x^67 -40042*x^66 -23120*x^65 -16553*x^64 -2740*x^63 -67288*x^62 +12645*x^61 -36909*x^60 -15108*x^59 -29676*x^58 +5532*x^57 -59246*x^56 +11419*x^55 -38227*x^54 -17035*x^53 -8823*x^52 -5830*x^51 -51778*x^50 +14876*x^49 -33907*x^48 -11207*x^47 -16396*x^46 +1203*x^45 -39478*x^44 +9466*x^43 -27926*x^42 -11499*x^41 -2969*x^40 -4679*x^39 -33324*x^38 +13644*x^37 -23042*x^36 -6948*x^35
-6260*x^34 -166*x^33 -21082*x^32 +5451*x^31 -14774*x^30 -5529*x^29 -472*x^28 -1184*x^27 -15956*x^26 +7833*x^25 -11110*x^24 -3505*x^23 -1570*x^22 -26*x^21 -7404*x^20 +2485*x^19 -5659*x^18 -744*x^17 -911*x^16 -88*x^15 -3949*x^14 +1706*x^13 -2502*x^12 -836*x^11 -494*x^10 +557*x^9 -1645*x^8 +928*x^7 -1496*x^6 +554*x^5 -650*x^4 +60*x^3 -89*x^2 -1) /
(-x^136 +x^135 -x^134 +x^132 -x^131 -x^128 -2*x^124 +2*x^123 -2*x^122 -x^121 +2*x^120 -2*x^119 -x^118 +x^117 -3*x^116 +x^115 -x^114 -2*x^112 +x^111 -2*x^110 -2*x^109 +2*x^108 -2*x^107 -2*x^106 +2*x^105 -5*x^104 +2*x^103 -2*x^102 -x^101 -x^99 -2*x^98 -x^97 -x^95 -2*x^94 +2*x^93
-5*x^92 +2*x^91 -2*x^90 -2*x^89 +2*x^88 -2*x^87 -2*x^86 +x^85 -2*x^84 -x^82 +x^81 -3*x^80 +x^79 -x^78 -2*x^77 +3*x^76 -2*x^75 -x^74 +2*x^73 -3*x^72 +x^71 -x^65 +3*x^64 -2*x^63 +x^62 +2*x^61 -3*x^60 +2*x^59 +x^58 -x^57 +3*x^56 -x^55 +x^54 +2*x^52 -x^51 +2*x^50 +2*x^49 -2*x^48 +2*x^47 +2*x^46
-2*x^45 +5*x^44 -2*x^43 +2*x^42 +x^41 +x^39 +2*x^38 +x^37 +x^35 +2*x^34 -2*x^33 +5*x^32 -2*x^31 +2*x^30 +2*x^29 -2*x^28 +2*x^27 +2*x^26 -x^25 +2*x^24 +x^22 -x^21 +3*x^20 -x^19 +x^18 +2*x^17 -2*x^16 +x^15 +2*x^14 -2*x^13 +2*x^12 +x^8 +x^5 -x^4 +x^2 -x +1):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..100);
CROSSREFS
Row n=10 of A220122.
Sequence in context: A166321 A187812 A075483 * A301827 A262093 A033409
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Dec 06 2012
STATUS
approved