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A364155 Number of tilings of a 4 X n rectangle using dominoes and trominoes (of any shape). 2
1, 1, 17, 145, 1294, 12109, 110017, 1014847, 9329739, 85734771, 788413732, 7247507779, 66631267902, 612575544564, 5631666716170, 51774765284018, 475989775503935, 4376002308955898, 40230688543323077, 369859957740214272, 3400299804915728832, 31260584166252805100 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
Wikipedia, Tromino
Index entries for linear recurrences with constant coefficients, signature (4, 34, 110, 107, 471, -389, -2708, 3428, -4181, -11740, 3747, -10113, -29419, 70950, 267918, -248892, 432693, -725427, 191447, -1184726, 1684957, -1052686, 1530485, -1038032, 837283, -1626500, 1230186, -380907, 255066, -430738, 319226, -125242, 49641, -8350, 11151, -15891, 2947, 584, 124, -160, 181, -11, -16, -4, 1).
FORMULA
G.f.: -(4*x^48 -15*x^47 -68*x^46 -60*x^45 +713*x^44 -459*x^43 +335*x^42 +2463*x^41 +12370*x^40 -60590*x^39 +28693*x^38 -22202*x^37 +189535*x^36 -450520*x^35 +1150691*x^34 -1400058*x^33 +584615*x^32 -1251182*x^31 +4498492*x^30 -5254375*x^29 +1720938*x^28 -3197095*x^27 +4899768*x^26 -2638295*x^25 +5588004*x^24 -2873134*x^23 -489180*x^22 -2469550*x^21 +842560*x^20 -609116*x^19 +705223*x^18 +618859*x^17 -72209*x^16 -18191*x^15 +30674*x^14 -50598*x^13 -34222*x^12 +10726*x^11 -8865*x^10 -7204*x^9 +3077*x^8 -308*x^7 +266*x^6 +445*x^5 +81*x^4 +67*x^3 +21*x^2 +3*x -1) / (-x^45 +4*x^44 +16*x^43 +11*x^42 -181*x^41 +160*x^40 -124*x^39 -584*x^38 -2947*x^37 +15891*x^36 -11151*x^35 +8350*x^34 -49641*x^33 +125242*x^32 -319226*x^31 +430738*x^30 -255066*x^29 +380907*x^28 -1230186*x^27 +1626500*x^26 -837283*x^25 +1038032*x^24 -1530485*x^23 +1052686*x^22 -1684957*x^21 +1184726*x^20 -191447*x^19 +725427*x^18 -432693*x^17 +248892*x^16 -267918*x^15 -70950*x^14 +29419*x^13 +10113*x^12 -3747*x^11 +11740*x^10 +4181*x^9 -3428*x^8 +2708*x^7 +389*x^6 -471*x^5 -107*x^4 -110*x^3 -34*x^2 -4*x +1).
EXAMPLE
a(2) = 17:
.___. .___. .___. .___. .___. .___. .___. .___. .___.
| | | |___| |___| | | | |___| |___| | | | | ._| |_. |
| | | | | | |___| |_|_| | | | |___| |_|_| |_| | | |_|
|_|_| | | | |___| |___| |_|_| | | | | | | |___| |___|
|___| |_|_| |___| |___| |___| |_|_| |_|_| |___| |___|
.
.___. .___. .___. .___. .___. .___. .___. .___.
|___| |___| | | | | | | |_. | | ._| |_. | | ._|
| ._| |_. | | |_| |_| | | |_| |_| | | |_| |_| |
|_| | | |_| |_| | | |_| | | | | | | |_| | | |_|
|___| |___| |___| |___| |_|_| |_|_| |___| |___| .
CROSSREFS
Column k=4 of A364457.
Sequence in context: A241796 A181908 A233328 * A083294 A196780 A208506
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Jul 28 2023
STATUS
approved

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Last modified February 28 07:05 EST 2024. Contains 370387 sequences. (Running on oeis4.)