A334180 - OEIS

%I #15 Dec 20 2024 20:43:15

%S 1,47,4271,434657,46069729,4974089647,541714928431,59235304882177,

%T 6489376893239297,711542422708907311,78049793235712789423,

%U 8562932336475599244257,939528644055272842890721,103089508033934831216777903,11311669427350891385087911471

%N Number of dimer tilings of a 2*n x 8 Moebius strip.

%F a(n)^2 = 4^n * Resultant(U_{2*n}(x/2), T_{8}(i*x/2)), where T_n(x) is a Chebyshev polynomial of the first kind, U_n(x) is a Chebyshev polynomial of the second kind and i = sqrt(-1).

%t a[n_] := 2^n * Sqrt[Resultant[ChebyshevU[2*n, x/2], ChebyshevT[8, I*x/2], x]]; Array[a, 15, 0] (* _Amiram Eldar_, May 04 2021 *)

%o (PARI) {a(n) = sqrtint(4^n*polresultant(polchebyshev(2*n, 2, x/2), polchebyshev(8, 1, I*x/2)))}

%Y Column 4 of A103997.

%Y Column 8 of A334178.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Apr 17 2020