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A220123 Number of tilings of a 4 X n rectangle using integer-sided rectangular tiles of area 4.

%I A220123 #48 Aug 31 2022 09:08:28
%S A220123 1,1,2,3,9,16,35,65,143,281,590,1174,2440,4925,10142,20563,42178,
%T A220123 85819,175632,357875,731536,1491966,3047879,6218844,12699982,25919176,
%U A220123 52922491,108022099,220541999,450186874,919074255,1876149465,3830134125,7818778884,15961716918
%N A220123 Number of tilings of a 4 X n rectangle using integer-sided rectangular tiles of area 4.
%H A220123 Alois P. Heinz, <a href="/A220123/b220123.txt">Table of n, a(n) for n = 0..1000</a>
%H A220123 Caleb Wagner, <a href="/A220123/a220123_1.pdf">Number of tilings of a 4 X n rectangle using integer sided rectangular tiles of area 4</a>, Nov 2013
%H A220123 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,5,-1,1,0,-1).
%F A220123 G.f.: -(x-1)*(x+1)*(x^2+1) / (x^8 - x^6 + x^5 - 5*x^4 - x^2 - x + 1).
%F A220123 a(n) = a(n-1) + a(n-2) + 5*a(n-4) - a(n-5) + a(n-6) - a(n-8). - _Caleb Wagner_, Nov 06 2013
%F A220123 a(2*n+1) = Sum_{k=0..n} A005178(k+1)*a(2*n-2*k). - _Shravan Haribalaraman_, Aug 29 2022
%e A220123 a(3) = 3, because there are 3 tilings of a 4 X 3 rectangle using integer-sided rectangular tiles of area 4:
%e A220123 ._._._.   ._.___.   .___._.
%e A220123 | | | |   | |   |   |   | |
%e A220123 | | | |   | |___|   |___| |
%e A220123 | | | |   | |   |   |   | |
%e A220123 |_|_|_|   |_|___|   |___|_|
%p A220123 gf:= -(x-1)*(x+1)*(x^2+1)/(x^8-x^6+x^5-5*x^4-x^2-x+1):
%p A220123 a:= n-> coeff(series(gf, x, n+1), x, n):
%p A220123 seq(a(n), n=0..50);
%Y A220123 Column k=4 of A220122. Cf. A005178.
%K A220123 nonn,easy
%O A220123 0,3
%A A220123 _Alois P. Heinz_, Dec 05 2012