A220135 Number of tilings of an n X 10 rectangle using integer-sided rectangular tiles of area n.

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

Alois P. Heinz, Table of n, a(n) for n = 0..2520

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

Adjacent sequences: A220132 A220133 A220134 * A220136 A220137 A220138

Keyword

nonn,easy

Author

Alois P. Heinz, Dec 06 2012

Status

approved