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%I #8 Sep 05 2021 22:00:54
%S 0,6,96,654,4938,33502,221672,1426734,9014839,56128696,345447208,
%T 2106033948,12739126739,76548375758,457375097789,2719454021744,
%U 16100269337597,94961606031670,558226473615469,3271710478901046,19123726111508773,111510459865449832
%N Number of squares in all tilings of a 6 X n rectangle using integer-sided square tiles.
%H Alois P. Heinz, <a href="/A226549/b226549.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: (4*x^23 +60*x^22 +203*x^21 +308*x^20 -35*x^19 -660*x^18 -964*x^17 -612*x^16 +239*x^15 +344*x^14 +683*x^13 +686*x^12 +1156*x^11 +1944*x^10 -341*x^9 -2280*x^8 -1775*x^7 +588*x^6 +1550*x^5 +70*x^4 -498*x^3 -48*x^2 +60*x+6)*x / (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)^2.
%Y Column k=6 of A226545.
%Y Cf. A219925.
%K nonn,easy
%O 0,2
%A _Alois P. Heinz_, Jun 10 2013
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