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

0,2

Links

Andrew Howroyd, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (194,-11392,260542, -2921984,18115138,-65660800, 142138174,-184101886,142138174, -65660800,18115138,-2921984, 260542,-11392,194,-1).

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).

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 *)

Prog

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

Crossrefs

Column 4 of A103997.

Column 8 of A334178.

Sequence in context: A123798 A104069 A389950 * A194617 A217229 A217230

Adjacent sequences: A334177 A334178 A334179 * A334181 A334182 A334183

Keyword

nonn

Author

Seiichi Manyama, Apr 17 2020

Status

approved