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

0,2

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

Formula

G.f.: see Maple program.

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 +32569667881308*x^8 -2274379347082*x^7 +121717789540*x^6 -4898404600*x^5 +144102468*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 +57526055007906*x^8 -3794064844276*x^7 +191447789306*x^6 -7247125678*x^5 +199881354*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);

Crossrefs

Column m=6 of A116694.

Sequence in context: A111923 A136246 A248074 * A264115 A113500 A064018

Adjacent sequences: A220296 A220297 A220298 * A220300 A220301 A220302

Keyword

nonn

Author

Alois P. Heinz, Dec 10 2012

Status

approved