A334182 Number of dimer tilings of a 2*n x 12 Moebius strip.

1, 322, 276119, 275770321, 289625349454, 312007855309063, 341133743251787719, 376320092633385077198, 417378876015895466713681, 464421220758849403137304663, 517771128105959394949223994178, 577920313480485996169789045855489, 645503767039127463811947619425652481

Offset

0,2

Links

Table of n, a(n) for n=0..12.

Formula

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).

Mathematica

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 *)

Prog

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

Crossrefs

Column 6 of A103997.

Column 12 of A334178.

Sequence in context: A234704 A266885 A253368 * A033524 A309030 A337781

Adjacent sequences: A334179 A334180 A334181 * A334183 A334184 A334185

Keyword

nonn,changed

Author

Seiichi Manyama, Apr 17 2020

Status

approved