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 A174248 Number of tilings of a 4 X n rectangle with n tetrominoes of any shape. 18
 1, 1, 4, 23, 117, 454, 2003, 9157, 40899, 179399, 796558, 3546996, 15747348, 69834517, 310058192, 1376868145, 6112247118, 27132236455, 120453362938, 534754586459, 2373975139658, 10538953415410, 46786795734201, 207705902269424, 922089495910044, 4093525019450760 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 S. Butler, J. Ekstrand, S. Osborne, TETRIS Tiling, AMS Spring Central Sectional, Iowa State University, April 27-28 2013 R. S. Harris, Counting Nonomino Tilings and Other Things of that Ilk, G4G9 Gift Exchange book, 2010. R. S. Harris, Counting Polyomino Tilings Wikipedia, Tetris Wikipedia, Tetromino FORMULA 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 CROSSREFS Cf. A134438, A174249, A226322, A232497, A232684, A232698, A232722, A233191, A233266. Column k=4 of A230031. Sequence in context: A306669 A124507 A239813 * A297309 A201350 A015532 Adjacent sequences:  A174245 A174246 A174247 * A174249 A174250 A174251 KEYWORD nonn,easy AUTHOR Bob Harris (me13013(AT)gmail.com), Mar 13 2010 EXTENSIONS a(0) inserted, a(11)-a(22) from Alois P. Heinz, May 07 2013 a(23)-a(25) from Alois P. Heinz, Nov 26 2013 STATUS approved

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Last modified May 9 13:42 EDT 2021. Contains 343742 sequences. (Running on oeis4.)