A220131 - OEIS

%I #14 Sep 05 2021 19:18:37

%S 1,1,13,6,35,3,46,1,35,6,15,1,88,1,13,8,35,1,46,1,37,6,13,1,88,3,13,6,

%T 35,1,48,1,35,6,13,3,88,1,13,6,37,1,46,1,35,8,13,1,88,1,15,6,35,1,46,

%U 3,35,6,13,1,90,1,13,6,35,3,46,1,35,6,15,1,88,1,13

%N Number of tilings of an n X 6 rectangle using integer-sided rectangular tiles of area n.

%C 1 followed by period 60: (1, 13, ..., 90) repeated; offset 0.

%H Alois P. Heinz, <a href="/A220131/b220131.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: see Maple program.

%e a(3) = 6, because there are 6 tilings of a 3 X 6 rectangle using integer-sided rectangular tiles of area 3:

%e ._._._._._._.   ._____._._._.   ._._____._._.

%e | | | | | | |   |_____| | | |   | |_____| | |

%e | | | | | | |   |_____| | | |   | |_____| | |

%e |_|_|_|_|_|_|   |_____|_|_|_|   |_|_____|_|_|

%e ._._._____._.   ._._._._____.   ._____._____.

%e | | |_____| |   | | | |_____|   |_____|_____|

%e | | |_____| |   | | | |_____|   |_____|_____|

%e |_|_|_____|_|   |_|_|_|_____|   |_____|_____|

%p gf:= -(89*x^16 +90*x^15 +103*x^14 +109*x^13 +144*x^12 +58*x^11 +103*x^10 +91*x^9 +120*x^8 +91*x^7 +103*x^6 +58*x^5 +56*x^4 +21*x^3 +15*x^2 +2*x +1) / (x^16 +x^15 +x^14 +x^13 +x^12 -x^4 -x^3 -x^2 -x -1):

%p a:= n-> coeff(series(gf, x, n+1), x, n):

%p seq(a(n), n=0..100);

%Y Row n=6 of A220122.

%K nonn,easy

%O 0,3

%A _Alois P. Heinz_, Dec 06 2012