A334180 Number of dimer tilings of a 2*n x 8 Moebius strip.
1, 47, 4271, 434657, 46069729, 4974089647, 541714928431, 59235304882177, 6489376893239297, 711542422708907311, 78049793235712789423, 8562932336475599244257, 939528644055272842890721, 103089508033934831216777903, 11311669427350891385087911471
Offset: 0
Keywords
Programs
-
Mathematica
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 *)
-
PARI
{a(n) = sqrtint(4^n*polresultant(polchebyshev(2*n, 2, x/2), polchebyshev(8, 1, I*x/2)))}
Formula
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).