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

0,3

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

Links

Table of n, a(n) for n=0..15.

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.

Crossrefs

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

Sequence in context: A200427 A250678 A178269 * A183588 A168220 A293105

Adjacent sequences: A351321 A351322 A351323 * A351325 A351326 A351327

Keyword

nonn,easy

Author

Gerhard Kirchner, Feb 21 2022

Status

approved