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A226373 Number of tilings of a 9 X n rectangle using integer-sided square tiles of area > 1.

%I A226373 #14 Sep 05 2021 21:59:55
%S A226373 1,0,0,1,0,0,19,0,0,50,17,0,499,34,2,1932,901,4,14152,2904,455,66283,
%T A226373 37037,1319,420837,158496,33772,2165069,1414662,133691,12858197,
%U A226373 7114650,1842975,69205389,52535381,8951317,398719444,288028604,88120788,2192096580
%N A226373 Number of tilings of a 9 X n rectangle using integer-sided square tiles of area > 1.
%H A226373 Alois P. Heinz, <a href="/A226373/b226373.txt">Table of n, a(n) for n = 0..1000</a>
%F A226373 G.f.: see Maple program.
%e A226373 a(14) = 2:
%e A226373 ._._._._._._._._._._._._._._.   ._._._._._._._._._._._._._._.
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%e A226373 |_____________|_____________|   |             |             |
%e A226373 |   |   |   |   |   |   |   |   |             |             |
%e A226373 |___|___|___|___|___|___|___|   |_____________|_____________|
%p A226373 a:= n-> coeff(series(-(6*x^47 -2*x^46 -6*x^45 +14*x^44 -4*x^43 -48*x^42 -7*x^41 +33*x^40 -61*x^39 -13*x^38 +62*x^37 +58*x^36 -20*x^35 -24*x^34 +30*x^33 -61*x^32 +18*x^31 +121*x^30 +86*x^29 -79*x^28 +270*x^27 +123*x^26 -134*x^25 -435*x^24 -113*x^23 +106*x^22 -388*x^21 -83*x^20 +66*x^19 +367*x^18 +60*x^17
%p A226373 -38*x^16 +189*x^15 +22*x^14 -8*x^13 -130*x^12 -13*x^11 +4*x^10 -36*x^9 -2*x^8 +20*x^6 +x^5 +2*x^3 -1) / (2*x^57 -4*x^55 +4*x^54 +2*x^53 -20*x^52 -75*x^51 +28*x^50 +18*x^49 -156*x^48 +89*x^47 +182*x^46 +88*x^45 -129*x^44 +225*x^43 -102*x^42 -53*x^41 -82*x^40 +346*x^39 +176*x^38 -573*x^37 -357*x^36 -242*x^35
%p A226373 +563*x^34 -583*x^33 +460*x^32 -121*x^31 +700*x^30 +8*x^29 +56*x^28 -2274*x^27 -872*x^26 +949*x^25 +1358*x^24 +368*x^23 -530*x^22 +2250*x^21 +394*x^20 -412*x^19 -1366*x^18 -200*x^17 +204*x^16 -694*x^15 -60*x^14 +46*x^13 +386*x^12 +29*x^11 -21*x^10 +79*x^9 +3*x^8 -36*x^6 -x^5 -3*x^3 +1), x, n+1), x, n):
%p A226373 seq(a(n), n=0..50);
%Y A226373 Column k=9 of A226206.
%K A226373 nonn,easy
%O A226373 0,7
%A A226373 _Alois P. Heinz_, Jun 05 2013