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A362298 Number of tilings of a 4 X n rectangle using dominos and 2 X 2 right triangles.

%I A362298 #11 Apr 28 2023 20:15:39
%S A362298 1,1,19,55,472,2023,13249,66325,392299,2088856,11877025,64803157,
%T A362298 362823607,1998759703,11123273896,61509329983,341492705365,
%U A362298 1891193243713,10489893539203,58127214942544,322296397820593,1786338231961609,9903234373856059,54893955008138983
%N A362298 Number of tilings of a 4 X n rectangle using dominos and 2 X 2 right triangles.
%C A362298 Triangles only occur as pairs forming 2 X 2 squares. For program code and additional details, see A362297.
%H A362298 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (4,18,-48,-42,99).
%F A362298 a(n) = 4*a(n-1) + 18*a(n-2) - 48*a(n-3) - 42*a(n-4) + 99*a(n-5).
%F A362298 G.f.: (9*x^3-3*x^2-3*x+1)/(-99*x^5+42*x^4+48*x^3-18*x^2-4*x+1).
%e A362298 a(2) = 19.
%e A362298 Partitions of a 2 X 2 square (triangles or dominos):
%e A362298    ___    ___    ___    ___
%e A362298   |  /|  |\  |  |___|  | | |
%e A362298   |/__|  |__\|  |___|  |_|_|
%e A362298        2t            2d
%e A362298    ___ ___    ___ ___    ___ ___    _ ___ _    _______
%e A362298   |2t |2t |  |2t |2d |  |2d |2t |  | |2t | |  |only d |
%e A362298   |___|___|  |___|___|  |___|___|  |_|___|_|  |_______|
%e A362298     4 ways +   4 ways +  4 ways  +   2 ways +  5 ways  = 19 ways
%e A362298 Only dominos: A005178(3) = 5.
%t A362298 LinearRecurrence[{4,18,-48,-42,99},{1,1,19,55,472},24] (* _Stefano Spezia_, Apr 20 2023 *)
%Y A362298 Column k=2 of A362297.
%Y A362298 Cf. A351322, A352432, A352433, A006130, A362299.
%K A362298 nonn,easy
%O A362298 0,3
%A A362298 _Gerhard Kirchner_, Apr 19 2023