A278875 Number of tilings of a 3 X n rectangle using pentominoes of any shape and monominoes.

1, 1, 7, 50, 311, 1954, 11914, 76003, 467221, 2943211, 18261840, 114360149, 712196192, 4449548684, 27749537725, 173227638835, 1080825788517, 6745415139188, 42092502492537, 262680587755837, 1639226363457986, 10229514197548963, 63836523795617745

Offset: 0

Author

Alois P. Heinz, Nov 29 2016

Keywords

• nonn
• easy

Examples

			a(2) = 7:
.___.  .___.  .___.  .___.  .___.  .___.  .___.
|_|_|  |   |  |   |  | |_|  |_| |  | ._|  |_. |
|_|_|  | ._|  |_. |  |   |  |   |  | |_|  |_| |
|_|_|  |_|_|  |_|_|  |___|  |___|  |___|  |___| .
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Wikipedia, Pentomino

Crossrefs

Column k=3 of A278657.

Formula

G.f.: -(x^70 +9*x^66 -58*x^65 +2*x^64 +33*x^62 -442*x^61 +1350*x^60 +177*x^59 +x^58 -1800*x^57 +7590*x^56 -14372*x^55 -5301*x^54 -4274*x^53 +27565*x^52 -57859*x^51 +81976*x^50 +25142*x^49 +52927*x^48 -178142*x^47 +267283*x^46 -286938*x^45 +18226*x^44 -271940*x^43 +645655*x^42 -741357*x^41 +769892*x^40 -399635*x^39 +731247*x^38 -1389200*x^37 +1406759*x^36 -1517890*x^35 +1113060*x^34 -1250164*x^33 +1807581*x^32 -1790865*x^31 +1917897*x^30 -1559114*x^29 +1282018*x^28 -1412376*x^27 +1442106*x^26 -1364028*x^25 +1161216*x^24 -797934*x^23 +646269*x^22 -590362*x^21 +518438*x^20 -428452*x^19 +276264*x^18 -167608*x^17 +99537*x^16 -80445*x^15 +63323*x^14 -44329*x^13 +18699*x^12 -9385*x^11 -862*x^10 -2736*x^9 -120*x^8 -534*x^7 -609*x^6 -199*x^5 -37*x^4 -13*x^3 -16*x^2 +1)

/ (x^75 +10*x^71 -67*x^70 +21*x^67 -575*x^66 +1781*x^65 +497*x^64 -87*x^63 -1909*x^62 +11113*x^61 -20753*x^60 -13155*x^59 -6937*x^58 +36701*x^57 -96686*x^56 +136888*x^55 +78888*x^54 +85389*x^53 -331892*x^52 +555027*x^51 -523802*x^50 -79591*x^49 -653455*x^48 +1705482*x^47 -1806940*x^46 +1752446*x^45 -1137530*x^44 +2652875*x^43 -4859649*x^42 +4471399*x^41 -5140040*x^40 +4864686*x^39 -6183059*x^38 +9006019*x^37 -8490050*x^36 +9607056*x^35 -9441593*x^34 +8984384*x^33 -10781348*x^32 [phone]*x^31 -10736664*x^30 [phone]*x^29 -7885992*x^28 +8169411*x^27 -7730756*x^26 +6657930*x^25 -5913652*x^24 +4235643*x^23 -3306372*x^22 +2709439*x^21 -2366644*x^20 +1645722*x^19 -1148473*x^18 +713958*x^17 -384641*x^16 +318569*x^15 -200025*x^14 +134362*x^13 -53508*x^12 +39041*x^11 -2080*x^10 +6477*x^9 +903*x^8 +1940*x^7 +863*x^6 +394*x^5 +110*x^4 +34*x^3 +22*x^2 +x -1).