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A226550 Number of squares in all tilings of a 7 X n rectangle using integer-sided square tiles. 3

%I

%S 0,7,180,1625,16936,157279,1426734,12582472,108971358,929801662,

%T 7842704798,65526395993,543197940936,4473218574611,36628689696182,

%U 298465716569236,2421637058537566,19574314969125483,157692516088571216,1266593481935599039,10146033357194978996

%N Number of squares in all tilings of a 7 X n rectangle using integer-sided square tiles.

%H Alois P. Heinz, <a href="/A226550/b226550.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: (36*x^42 +492*x^41 +97*x^40 -1280*x^39 +1374*x^38 +3986*x^37 -3294*x^36 -12844*x^35 -17178*x^34 -5612*x^33 -8231*x^32 -68874*x^31 -38198*x^30 +87106*x^29 +79120*x^28 +342382*x^27 +1028045*x^26 +1129834*x^25 +797531*x^24 +933000*x^23 +781401*x^22 -15364*x^21 -688028*x^20 -1167490*x^19 -1199056*x^18 -495108*x^17 +175219*x^16 +637592*x^15 +810642*x^14 +590608*x^13 +255600*x^12 -62792*x^11 -226422*x^10 -130944*x^9 -26229*x^8 +21996*x^7 +25573*x^6 +5782*x^5 -3711*x^4 -1682*x^3 +174*x^2 +138*x+7)*x / (6*x^25 +11*x^24 -9*x^23 -10*x^22 +39*x^21 +12*x^20 -70*x^19 -281*x^18 -403*x^17 -110*x^16 -118*x^15 -790*x^14 -179*x^13 +466*x^12 +327*x^11 +669*x^10 +1028*x^9 +231*x^8 -45*x^7 -284*x^6 -273*x^5 -61*x^4 +45*x^3 +31*x^2 +3*x-1)^2.

%Y Column k=7 of A226545.

%Y Cf. A219926.

%K nonn,easy

%O 0,2

%A _Alois P. Heinz_, Jun 10 2013

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Last modified September 27 13:17 EDT 2021. Contains 347688 sequences. (Running on oeis4.)