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A220131 Number of tilings of an n X 6 rectangle using integer-sided rectangular tiles of area n.

%I A220131 #14 Sep 05 2021 19:18:37
%S A220131 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 A220131 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 A220131 3,35,6,13,1,90,1,13,6,35,3,46,1,35,6,15,1,88,1,13
%N A220131 Number of tilings of an n X 6 rectangle using integer-sided rectangular tiles of area n.
%C A220131 1 followed by period 60: (1, 13, ..., 90) repeated; offset 0.
%H A220131 Alois P. Heinz, <a href="/A220131/b220131.txt">Table of n, a(n) for n = 0..1000</a>
%F A220131 G.f.: see Maple program.
%e A220131 a(3) = 6, because there are 6 tilings of a 3 X 6 rectangle using integer-sided rectangular tiles of area 3:
%e A220131 ._._._._._._.   ._____._._._.   ._._____._._.
%e A220131 | | | | | | |   |_____| | | |   | |_____| | |
%e A220131 | | | | | | |   |_____| | | |   | |_____| | |
%e A220131 |_|_|_|_|_|_|   |_____|_|_|_|   |_|_____|_|_|
%e A220131 ._._._____._.   ._._._._____.   ._____._____.
%e A220131 | | |_____| |   | | | |_____|   |_____|_____|
%e A220131 | | |_____| |   | | | |_____|   |_____|_____|
%e A220131 |_|_|_____|_|   |_|_|_|_____|   |_____|_____|
%p A220131 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 A220131 a:= n-> coeff(series(gf, x, n+1), x, n):
%p A220131 seq(a(n), n=0..100);
%Y A220131 Row n=6 of A220122.
%K A220131 nonn,easy
%O A220131 0,3
%A A220131 _Alois P. Heinz_, Dec 06 2012