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A189003 Number of domino tilings of the 5 X n grid with upper left corner removed iff n is odd.

%I A189003 #24 Jul 07 2020 04:22:37
%S A189003 1,1,8,15,95,192,1183,2415,14824,30305,185921,380160,2332097,4768673,
%T A189003 29253160,59817135,366944287,750331584,4602858719,9411975375,
%U A189003 57737128904,118061508289,724240365697,1480934568960,9084693297025,18576479568193,113956161827912
%N A189003 Number of domino tilings of the 5 X n grid with upper left corner removed iff n is odd.
%H A189003 Alois P. Heinz, <a href="/A189003/b189003.txt">Table of n, a(n) for n = 0..550</a>
%H A189003 <a href="/index/Do#domino">Index entries for sequences related to dominoes</a>
%H A189003 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,15,0,-32,0,15,0,-1).
%F A189003 G.f.: (x-1)*(1+x)*(x^4+x^3-6*x^2+x+1) / (-x^8+15*x^6-32*x^4+15*x^2-1).
%p A189003 a:= n-> (<<0|1|0|0>, <0|0|1|0>, <0|0|0|1>, <-1|15|-32|15>>^iquo(n, 2, 'r').
%p A189003         `if`(r=0, <<8, 1, 1, 8>>, <<1, 0, 1, 15>>))[3, 1]:
%p A189003 seq(a(n), n=0..30);
%t A189003 a[n_] := Product[2(2+Cos[2 j Pi/(n+1)]+Cos[k Pi/3]), {k, 1, 2}, {j, 1, n/2} ] // Round;
%t A189003 Table[a[n], {n, 0, 24}] (* _Jean-François Alcover_, Aug 19 2018, after A099390 *)
%Y A189003 5th row of array A189006.
%Y A189003 Bisections give: A003775 (even part), A006238 (odd part).
%K A189003 nonn,easy
%O A189003 0,3
%A A189003 _Alois P. Heinz_, Apr 15 2011