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A352433 Number of tilings of a 5 X 2n rectangle using dominoes and 2 X 2 tiles.

%I A352433 #26 Jul 05 2024 14:11:47
%S A352433 1,21,593,17937,550969,16982489,523857737,16162268361,498665065833,
%T A352433 15385785653481,474713270165161,14646818304387753,451913453451818281,
%U A352433 13943354204817352489,430208763273959521833,13273677023152591308329,409546519819086706020393
%N A352433 Number of tilings of a 5 X 2n rectangle using dominoes and 2 X 2 tiles.
%C A352433 The sequence is based on A352431.
%H A352433 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (51,-764,4822,-13756,17328,-7680). [Signs corrected by Georg Fischer, Sep 30 2022]
%F A352433 G.f.: (1 - 30*x + 286*x^2 - 1084*x^3 + 1728*x^4 - 960*x^5)/(1 - 51*x + 764*x^2 - 4822*x^3 + 13756*x^4 - 17328*x^5 + 7680*x^6).
%F A352433 a(n) = 51*a(n-1) - 764*a(n-2) + 4822*a(n-3) - 13756*a(n-4) + 17328*a(n-5) - 7680*a(n-6).
%e A352433 n=1: a(1)=21
%e A352433 The cells in the first row are covered by a horizontal domino, vertical dominoes or a square. The remaining rectangle has 11 (see example A352432) or 5 tilings.
%e A352433    ___    ___    ___                5 tilings of a 3 X 2 rectangle:
%e A352433   |___|  | | |  |   |                 ___   ___   ___   ___   ___
%e A352433   |   |  |_|_|  |___|                |   | |___| |___| | | | |___|
%e A352433   |   |  |   |  |   |                |___| |   | |___| |_|_| |___|
%e A352433   | 11|  | 5 |  | 5 |                |___| |___| |___| |___| |_|_|
%e A352433   |___|  |___|  |___|
%t A352433 LinearRecurrence[{51, -764, 4822, -13756, 17328, -7680}, {1, 21, 593, 17937, 550969, 16982489}, 17] (* _Hugo Pfoertner_, Sep 30 2022 *)
%o A352433 (PARI) Vec((1-30*x+286*x^2-1084*x^3+1728*x^4-960*x^5)/(1-51*x+764*x^2-4822*x^3+13756*x^4-17328*x^5+7680*x^6)+O(x^99)) \\ _Charles R Greathouse IV_, Jul 05 2024
%Y A352433 Cf. A352431, A352432.
%K A352433 nonn,easy
%O A352433 0,2
%A A352433 _Gerhard Kirchner_, Mar 17 2022