%I #17 Sep 05 2021 18:21:12

%S 1,1,13,60,348,1916,10668,59257,329350,1830234,10171315,56525022,

%T 314128014,1745708992,9701463927,53914132251,299618062228,

%U 1665073290365,9253344266757,51423790446062,285778433090830,1588162056821687,8825923956549044,49048479247236561

%N Number of tilings of a 6 X n rectangle using integer-sided square tiles.

%H Alois P. Heinz, <a href="/A219925/b219925.txt">Table of n, a(n) for n = 0..500</a>

%F G.f.: see Maple program.

%e a(2) = 13, because there are 13 tilings of a 6 X 2 rectangle using integer-sided square tiles:

%e ._._. .___. ._._. ._._. ._._. ._._.

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

%e |_|_| |___| | | |_|_| |_|_| |_|_|

%e |_|_| |_|_| |___| | | |_|_| |_|_|

%e |_|_| |_|_| |_|_| |___| | | |_|_|

%e |_|_| |_|_| |_|_| |_|_| |___| | |

%e |_|_| |_|_| |_|_| |_|_| |_|_| |___|

%e .___. .___. .___. ._._. ._._. ._._. .___.

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

%e |___| |___| |___| | | | | |_|_| |___|

%e | | |_|_| |_|_| |___| |___| | | | |

%e |___| | | |_|_| | | |_|_| |___| |___|

%e |_|_| |___| | | |___| | | | | | |

%e |_|_| |_|_| |___| |_|_| |___| |___| |___|

%p gf:= -(2*x^9 +3*x^8 +2*x^7 -3*x^6 -7*x^5 -4*x^4 -3*x^3 +5*x^2 +2*x -1) / (2*x^15 +7*x^14 +12*x^13 +6*x^12 -18*x^11 -13*x^10 -8*x^9 -27*x^8 -32*x^7 +x^6 +40*x^5 +34*x^4 -3*x^3 -15*x^2 -3*x +1):

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

%p seq (a(n), n=0..40);

%Y Column k=6 of A219924.

%Y Cf. A226549.

%K nonn,easy

%O 0,3

%A _Alois P. Heinz_, Dec 01 2012