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%I #23 May 04 2021 02:12:28
%S 1,7,71,769,8449,93127,1027207,11332097,125019649,1379271559,
%T 15216755911,167878292737,1852111179521,20433349871431,
%U 225430197438727,2487050546734081,27438295728380929,302712011022644999,3339659377008916807,36844671993005504257,406487518942362537217
%N Number of dimer tilings of a 2*n x 4 Moebius strip.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Chebyshev_polynomials">Chebyshev polynomials</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Resultant">Resultant</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (14,-34,14,-1).
%F a(n)^2 = 4^n * Resultant(U(2*n,x), 1+2*x^2+1/2*x^4), where U(n,x) is a Chebyshev polynomial of the second kind and i = sqrt(-1).
%F G.f.: ((1-x)*(1-6*x+x^2))/(1-14*x+34*x^2-14*x^3+x^4).
%F a(n) = 14*a(n-1) - 34*a(n-2) + 14*a(n-3) - a(n-4) for n > 3.
%t a[n_] := 2^n * Sqrt[Resultant[ChebyshevU[2*n, x/2], ChebyshevT[4, I*x/2], x]]; Array[a, 21, 0] (* _Amiram Eldar_, May 04 2021 *)
%o (PARI) a(n) = sqrtint(4^n*polresultant(polchebyshev(2*n, 2, x/2), 1+2*x^2+1/2*x^4))
%o (PARI) N=20; x='x+O('x^N); Vec(((1-x)*(1-6*x+x^2))/(1-14*x+34*x^2-14*x^3+x^4))
%Y Column 2 of A103997.
%K nonn,easy
%O 0,2
%A _Seiichi Manyama_, Apr 15 2020
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