A334181 Number of dimer tilings of a 2*n x 10 Moebius strip.

1, 123, 34276, 10894561, 3625549353, 1234496016491, 425588878897051, 147716667776449068, 51459452422736225401, 17962375573820654607091, 6276640725138515237851803, 2194525820018749279915303361, 767517569389298359121889024076, 268477550040900162034429991254323

Offset

0,2

Links

Table of n, a(n) for n=0..13.

Formula

a(n)^2 = 4^n * Resultant(U_{2*n}(x/2), T_{10}(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[10, I*x/2], x]]; Array[a, 14, 0] (* Amiram Eldar, May 04 2021 *)

Prog

(PARI) {a(n) = sqrtint(4^n*polresultant(polchebyshev(2*n, 2, x/2), polchebyshev(10, 1, I*x/2)))}

Crossrefs

Column 5 of A103997.

Column 10 of A334178.

Sequence in context: A181006 A362497 A289331 * A033522 A214464 A288353

Adjacent sequences: A334178 A334179 A334180 * A334182 A334183 A334184

Keyword

nonn

Author

Seiichi Manyama, Apr 17 2020

Status

approved