A334183 Number of dimer tilings of a 2*n x 14 Moebius strip.

1, 843, 2226851, 7009284232, 23313951730593, 79684937704014787, 276820366633357961907, 971684488369988888850993, 3433809783046699326165318697, 12187832583695135440208385490411, 43381711462091769247169214041784216, 154696550169813236996441805153918153313

Offset

0,2

Links

Table of n, a(n) for n=0..11.

Formula

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).

Mathematica

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 *)

Prog

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

Crossrefs

Column 7 of A103997.

Column 14 of A334178.

Sequence in context: A158403 A114359 A038013 * A078144 A071320 A338628

Adjacent sequences: A334180 A334181 A334182 * A334184 A334185 A334186

Keyword

nonn

Author

Seiichi Manyama, Apr 17 2020

Status

approved