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%I #43 Dec 04 2018 21:22:03
%S 1,1,4,23,117,454,2003,9157,40899,179399,796558,3546996,15747348,
%T 69834517,310058192,1376868145,6112247118,27132236455,120453362938,
%U 534754586459,2373975139658,10538953415410,46786795734201,207705902269424,922089495910044,4093525019450760
%N Number of tilings of a 4 X n rectangle with n tetrominoes of any shape.
%H Alois P. Heinz, <a href="/A174248/b174248.txt">Table of n, a(n) for n = 0..1000</a>
%H S. Butler, J. Ekstrand, S. Osborne, <a href="/A230031/a230031.pdf">TETRIS Tiling</a>, AMS Spring Central Sectional, Iowa State University, April 27-28 2013
%H R. S. Harris, <a href="http://www.bumblebeagle.org/polyominoes/tilingcounting/counting_9x9_tilings.pdf">Counting Nonomino Tilings and Other Things of that Ilk</a>, G4G9 Gift Exchange book, 2010.
%H R. S. Harris, <a href="http://www.bumblebeagle.org/polyominoes/tilingcounting">Counting Polyomino Tilings</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Tetris">Tetris</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Tetromino">Tetromino</a>
%F G.f.: -(x^31 +3*x^30 -2*x^29 -7*x^28 -25*x^27 -78*x^26 +23*x^25 +116*x^24 +217*x^23 +604*x^22 -21*x^21 -556*x^20 -649*x^19 -1621*x^18 -175*x^17 +727*x^16 +523*x^15 +1707*x^14 +236*x^13 -470*x^12 -143*x^11 -749*x^10 -133*x^9 +166*x^8 +15*x^7 +126*x^6 +27*x^5 -23*x^4 -x^3 -6*x^2 -x +1) / (x^35 +3*x^34 -3*x^33 -13*x^32 -50*x^31 -123*x^30 +39*x^29 +225*x^28 +659*x^27 +1476*x^26 +60*x^25 -1102*x^24 -2600*x^23 -6047*x^22 -489*x^21 +2786*x^20 +3210*x^19 +9566*x^18 +1102*x^17 -3349*x^16 -1620*x^15 -6885*x^14 -1053*x^13 +1970*x^12 +414*x^11 +2258*x^10 +469*x^9 -548*x^8 -76*x^7 -290*x^6 -77*x^5 +54*x^4 +8*x^3 +8*x^2 +2*x -1). - _Alois P. Heinz_, Nov 26 2013
%Y Cf. A134438, A174249, A226322, A232497, A232684, A232698, A232722, A233191, A233266.
%Y Column k=4 of A230031.
%K nonn,easy
%O 0,3
%A Bob Harris (me13013(AT)gmail.com), Mar 13 2010
%E a(0) inserted, a(11)-a(22) from _Alois P. Heinz_, May 07 2013
%E a(23)-a(25) from _Alois P. Heinz_, Nov 26 2013
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