A226371 - OEIS

%I #9 Sep 05 2021 21:59:39

%S 1,0,0,0,0,0,7,1,0,0,2,0,57,16,1,0,32,4,463,197,29,1,392,100,3767,

%T 2150,518,46,4267,1668,30763,21953,7454,1128,43531,23057,252755,

%U 215070,94769,20728,426847,285548,2094102,2050219,1112227,321677,4080855,3290655

%N Number of tilings of a 7 X n rectangle using integer-sided square tiles of area > 1.

%H Alois P. Heinz, <a href="/A226371/b226371.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: (-x^12-x^9+2*x^6+x^3-1) / (x^19 -x^18 -x^16 -x^15 -2*x^13 -7*x^12 +x^10 -8*x^9 +x^7 +9*x^6 +x^3-1).

%e a(10) = 2:

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

%e |         |         |   |   |   |   |   |   |

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

%e |         |         |   |         |         |

%e |         |         |   |         |         |

%e |_________|_________|   |         |         |

%e |   |   |   |   |   |   |         |         |

%e |___|___|___|___|___|   |_________|_________|

%p a:= n-> coeff(series((-x^12-x^9+2*x^6+x^3-1) / (x^19 -x^18 -x^16 -x^15 -2*x^13 -7*x^12 +x^10 -8*x^9 +x^7 +9*x^6 +x^3-1), x, n+1), x, n):

%p seq(a(n), n=0..70);

%Y Column k=7 of A226206.

%K nonn,easy

%O 0,7

%A _Alois P. Heinz_, Jun 05 2013