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%I #12 Feb 06 2017 12:35:42
%S 1,1,1,7,25,50,155,508,1343,3800,11438,32525,92333,268766,774302,
%T 2216976,6392865,18425916,52958070,152425812,438973764,1263109849,
%U 3634965137,10463959311,30116734921,86675829307,249478723992,718056248229,2066658063664,5948257601097
%N Number of tilings of a 2 X n rectangle using pentominoes of any shape and monominoes.
%H Alois P. Heinz, <a href="/A278874/b278874.txt">Table of n, a(n) for n = 0..1000</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Pentomino">Pentomino</a>
%F G.f.: -(x^10 +x^8 -x^6 -6*x^5 -x^4 -5*x^3 +1) / (x^15 +x^13 -2*x^11 -11*x^10 -2*x^9 -10*x^8 +x^7 +9*x^6 +12*x^5 +8*x^4 +11*x^3 +x -1).
%e a(3) = 7:
%e ._____. ._____. ._____. ._____. ._____. ._____. ._____.
%e |_|_|_| | |_| | | ._. | | ._| |_. | | |_| |_| |
%e |_|_|_| |_____| |_|_|_| |___|_| |_|___| |_____| |_____| .
%Y Column k=2 of A278657.
%K nonn,easy
%O 0,4
%A _Alois P. Heinz_, Nov 29 2016