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%I #17 May 14 2018 11:31:02
%S 1,2,4,8,45,248,1032,3524,13173,54274,228712,917992,3608665,14286188,
%T 57438652,231343468,926921081,3700936774,14793198332,59241396140,
%U 237333611629,950127617692,3801974385964,15215432779936,60907523900693,243826775063490,976008753961184
%N Number of tilings of a 4 X 4 X n box using 4n bricks of shape 4 X 1 X 1.
%H Alois P. Heinz, <a href="/A233291/b233291.txt">Table of n, a(n) for n = 0..1000</a>
%H R. J. Mathar, <a href="https://arxiv.org/abs/1406.7788">Tilings of rectangular regions by rectangular tiles: counts derived from transfer matrices</a>, arXiv:1406.7788 [math.CO], 2014; eq. (52).
%F G.f.: (x^31 -x^30 -x^29 -3*x^28 -5*x^27 +8*x^26 +3*x^25 -39*x^24 +48*x^23 +34*x^22 -11*x^21 +112*x^20 -63*x^19 -34*x^18 +166*x^17 -188*x^16 -174*x^15 +151*x^14 -251*x^13 +57*x^12 +104*x^11 +171*x^10 -69*x^9 -90*x^8 -30*x^7 -61*x^6 +20*x^5 +31*x^4 +4*x^3 +4*x^2 +x -1) / (-x^35 +x^34 +x^33 +5*x^32 +4*x^31 -11*x^30 -10*x^29 +54*x^28 -65*x^27 -48*x^26 -48*x^25 -195*x^24 +231*x^23 -78*x^22 -473*x^21 +794*x^20 +447*x^19 -981*x^18 +1285*x^17 +395*x^16 -720*x^15 -202*x^14 +640*x^13 +567*x^12 -232*x^11 +638*x^10 -169*x^9 -233*x^8 -256*x^7 -97*x^6 +29*x^5 +52*x^4 -4*x^3 +2*x^2 +3*x -1).
%Y Column k=4 of A233308.
%Y Cf. A006253, A233289, A233294.
%K nonn,easy
%O 0,2
%A _Alois P. Heinz_, Dec 06 2013
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