A334183 - OEIS

%I #14 Dec 21 2024 01:02:02

%S 1,843,2226851,7009284232,23313951730593,79684937704014787,

%T 276820366633357961907,971684488369988888850993,

%U 3433809783046699326165318697,12187832583695135440208385490411,43381711462091769247169214041784216,154696550169813236996441805153918153313

%N Number of dimer tilings of a 2*n x 14 Moebius strip.

%F a(n)^2 = 4^n * Resultant(U_{2*n}(x/2), T_{14}(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[14, I*x/2], x]]; Array[a, 12, 0] (* _Amiram Eldar_, May 04 2021 *)

%o (PARI) {a(n) = sqrtint(4^n*polresultant(polchebyshev(2*n, 2, x/2), polchebyshev(14, 1, I*x/2)))}

%Y Column 7 of A103997.

%Y Column 14 of A334178.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Apr 17 2020