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%I #19 Sep 05 2021 18:21:57
%S 1,1,34,277,3049,31497,329350,3435392,35863972,374285478,3906605183,
%T 40773605243,425562898029,4441677458152,46358636450427,
%U 483853831650209,5050074056261222,52708577944998395,550129399697072615,5741804607960538038,59928300863912394900
%N Number of tilings of an 8 X n rectangle using integer-sided square tiles.
%H Alois P. Heinz, <a href="/A219927/b219927.txt">Table of n, a(n) for n = 0..500</a>
%F G.f.: see Maple program.
%p gf:= -(60*x^40 +136*x^39 -321*x^38 -1038*x^37 -2045*x^36 +2501*x^35 +4393*x^34 +7347*x^33 +4372*x^32 -4825*x^31 -13838*x^30 -19585*x^29 -9331*x^28 -40213*x^27 +19891*x^26 +57417*x^25 +68058*x^24 +10427*x^23 -8789*x^22 +6040*x^21 -76684*x^20 -81024*x^19 -16484*x^18 +11908*x^17 +42083*x^16 +63711*x^15 +19938*x^14 -2290*x^13 -18240*x^12 -18560*x^11 -7633*x^10 +291*x^9 +4194*x^8 +2502*x^7 +378*x^6 -361*x^5 -240*x^4 -33*x^3 +27*x^2 +5*x -1) /
%p (60*x^48 +256*x^47 +35*x^46 -1488*x^45 -4435*x^44 -2543*x^43 +7032*x^42 +16610*x^41 +23043*x^40 +18924*x^39 +3186*x^38 -57091*x^37 -115830*x^36 -141242*x^35 +18849*x^34 +39846*x^33 +240064*x^32 +433164*x^31 +162501*x^30 -692061*x^29 -641988*x^28 +446013*x^27 +530385*x^26 +657974*x^25 -654746*x^24 -708014*x^23 -43614*x^22 -370550*x^21 +356235*x^20 +824516*x^19 +224413*x^18 -94736*x^17 -143852*x^16 -344353*x^15 -110166*x^14 +15107*x^13 +55317*x^12 +51581*x^11 +29259*x^10 +6818*x^9 -5977*x^8 -8807*x^7 -2453*x^6 +1175*x^5 +708*x^4 +15*x^3 -55*x^2 -6*x +1):
%p a:= n-> coeff(series(gf, x, n+1), x, n):
%p seq(a(n), n=0..30);
%Y Column k=8 of A219924.
%Y Cf. A226551.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Dec 01 2012
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