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

%I A351324 #26 May 02 2023 01:20:44
%S A351324 1,0,520,22656,1795360,115363072,7876120608,527256809600,
%T A351324 35522814546496,2388257605782016,160678147466414272,
%U A351324 10807663334085120512,727010169682181839360,48903265220016072792320,3289569236212332037229184,221278350342281369716796672
%N A351324 Number of tilings of a 7 X 3n rectangle with right trominoes.
%C A351324 See A351322 for algorithm.
%C A351324 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
%F A351324 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).
%F A351324 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.
%Y A351324 Cf. A077957, A000079, A046984, A084478, A351322, A351323, A236578 (straight trominoes), A233343 (mixed trominoes).
%K A351324 nonn,easy
%O A351324 0,3
%A A351324 _Gerhard Kirchner_, Feb 21 2022