A351324 Number of tilings of a 7 X 3n rectangle with right trominoes.

1, 0, 520, 22656, 1795360, 115363072, 7876120608, 527256809600, 35522814546496, 2388257605782016, 160678147466414272, 10807663334085120512, 727010169682181839360, 48903265220016072792320, 3289569236212332037229184, 221278350342281369716796672

Offset: 0

Author

Gerhard Kirchner, Feb 21 2022

Keywords

• nonn
• easy

Comments

See A351322 for algorithm.

This is the Hadamard sum of the following 4 sequences: 0, 0,0,0, 158208,.. (tilings which have both vertical and horizontal faults), 0,0,480,6144, 125952 ... (tilings which have horizontal faults but no vertical faults), 00,0,0,112192,.. (tilings which have vertical but no horizontal faults), 1, 0,40, 16512, 1399008 ,... (tilings which have neither horizontal nor vertical faults). - R. J. Mathar, Dec 08 2022

Crossrefs

Cf. A077957, A000079, A046984, A084478, A351322, A351323, A236578 (straight trominoes), A233343 (mixed trominoes).

Formula

G.f.: (1 - 22*x - 1831*x^2 - 29454*x^3 - 270630*x^4 - 2070388*x^5 - 12125943*x^6 - 48147976*x^7 - 151548064*x^8 - 417242784*x^9 - 423562924*x^10 + 586224672*x^11 + 915719344*x^12 + 349980800*x^13 + 371621248*x^14 - 6541312*x^15 - 9691136*x^16 + 589824*x^17)/(1 - 22*x - 2351*x^2 - 40670*x^3 - 345038*x^4 - 3522884*x^5 - 28528327*x^6 - 145350120*x^7 - 623982088*x^8 - 2110011040*x^9 - 1354478796*x^10 + 9281598624*x^11 + 15001687984*x^12 + 3456230016*x^13 - 3194643904*x^14 - 1637793792*x^15 - 575934464*x^16 + 65175552*x^17).

a(n) = 22*a(n-1) + 2351*a(n-2) + 40670*a(n-3) + 345038*a(n-4) + 3522884*a(n-5) + 28528327*a(n-6) + 145350120*a(n-7) + 623982088*a(n-8) + 2110011040*a(n-9) + 1354478796*a(n-10) - 9281598624*a(n-11) - 15001687984*a(n-12) - 3456230016*a(n-13) + 3194643904*a(n-14) + 1637793792*a(n-15) + 575934464*a(n-16) - 65175552*a(n-17) for n>16.