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%I #27 Dec 03 2022 11:24:49
%S 1,1,34,171,2115,16334,159651,1382259,12727570,113555791,1029574631,
%T 9258357134,83605623809,753361554685,6795928721858,61270295494859,
%U 552555688390363,4982395765808506,44929655655496287,405145692220245539,3653405881837027898
%N Number of ways to tile an 8 X n rectangle with 1 X 1 and 2 X 2 tiles.
%H S. Butler and S. Osborne, <a href="http://orion.math.iastate.edu/butler/papers/14_02_walks.pdf">Counting tilings by taking walks</a>, 2012. - From _N. J. A. Sloane_, Dec 27 2012
%H R. J. Mathar, <a href="https://arxiv.org/abs/1609.03964">Tiling nXm rectangles with 1X1 and sXs squares</a>, arXiv:1609.03964 (2016) Section 4.1
%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (6, 50, -171, -514, 1800, 845, -5430, 704, 6175, -1762, -2810, 870, 392, -120).
%F a(n) = 6a(n-1) + 50a(n-2) - 171a(n-3) - 514a(n-4) + 1800a(n-5) + 845a(n-6) - 5430a(n-7) + 704a(n-8) + 6175a(n-9) - 1762a(n-10) - 2810a(n-11) + 870a(n-12) + 392a(n-13) - 120a(n-14). - Keith Schneider (kschneid(AT)bulldog.unca.edu), Apr 02 2006
%F G.f.: ( 1 -5*x -22*x^2 +88*x^3 +74*x^4 -378*x^5 -31*x^6 +597*x^7 -114*x^8 -336*x^9 +94*x^10 +52*x^11 -16*x^12 ) / ( 1 -6*x -50*x^2 +171*x^3 +514*x^4 -1800*x^5 -845*x^6 +5430*x^7 -704*x^8 -6175*x^9 +1762*x^10 +2810*x^11 -870*x^12 -392*x^13 +120*x^14 ). - _R. J. Mathar_, Dec 19 2015
%Y Cf. A001045, A054854, A054855, A063650-A063654.
%Y Column k=8 of A245013.
%K nonn
%O 0,3
%A _Reiner Martin_, Jul 23 2001
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