A334182 - OEIS

%I #11 May 04 2021 02:10:02

%S 1,322,276119,275770321,289625349454,312007855309063,

%T 341133743251787719,376320092633385077198,417378876015895466713681,

%U 464421220758849403137304663,517771128105959394949223994178,577920313480485996169789045855489,645503767039127463811947619425652481

%N Number of dimer tilings of a 2*n x 12 Moebius strip.

%F a(n)^2 = 4^n * Resultant(U_{2*n}(x/2), T_{12}(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[12, I*x/2], x]]; Array[a, 13, 0] (* _Amiram Eldar_, May 04 2021 *)

%o (PARI) {a(n) = sqrtint(4^n*polresultant(polchebyshev(2*n, 2, x/2), polchebyshev(12, 1, I*x/2)))}

%Y Column 6 of A103997.

%Y Column 12 of A334178.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Apr 17 2020