A220299 Number of ways to cut a 6 X n rectangle into rectangles with integer sides.

1, 32, 2864, 314662, 36911922, 4427635270, 535236230270, 64878517290010, 7871769490695758, 955411617212520670, 115973945786899746170, 14078248409306427591814, 1709004742525016740261850, 207462778992946779638832746, 25184765957310295151583128422

Offset: 0

Author

Alois P. Heinz, Dec 10 2012

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..200
• David A. Klarner and Spyros S. Magliveras, The number of tilings of a block with blocks, European Journal of Combinatorics 9 (1988), 317-330.
• Joshua Smith and Helena Verrill, On dividing rectangles into rectangles

Crossrefs

Column m=6 of A116694.

Programs

Maple

gf:= (916798938728006656*x^20 -3962057190907156288*x^19 +7644699117821849592*x^18 -8795707489604640136*x^17 +6787540243858479914*x^16 -3741365942249935792*x^15 +1530293206620422033*x^14 -475918767335413756*x^13
+114321113226304761*x^12 -21415445169034874*x^11 +3143712388922139*x^10 -361909626897452*x^9 [phone]*x^8 -2274379347082*x^7 [phone]*x^6 -4898404600*x^5 [phone]*x^4 -2968032*x^3 +39908*x^2 -308*x +1)/
(3488260147244630016*x^20 -13785403213649739264*x^19 +24571927550599277952*x^18 -26305901575283773400*x^17 +18988035581731414180*x^16 -9828185761768234778*x^15
+3785664669818771697*x^14 -1111033817019987980*x^13 +252212834590208135*x^12 -44688005447169948*x^11 +6207093806210985*x^10 -676048684437666*x^9 [phone]*x^8 -3794064844276*x^7 [phone]*x^6 -7247125678*x^5 [phone]*x^4 -3842502*x^3 +47924*x^2 -340*x +1):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..20);

Formula

G.f.: see Maple program.