A334179 Number of dimer tilings of a 2*n x 6 Moebius strip.

1, 18, 539, 17753, 603126, 20721019, 714790675, 24693540102, 853526336417, 29507528240963, 1020183543633762, 35272351950083641, 1219535200106522761, 42165342386915661378, 1457865351514568764211, 50405667966576581717969, 1742775306265709714234214, 60256436430143085819341347

Offset

0,2

Links

Andrew Howroyd, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (52,-673,2548,-3856,2548,-673,52,-1).

Formula

a(n)^2 = 4^n * Resultant(U_{2*n}(x/2), T_{6}(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).

G.f.: (1 - x)*(1 - 33*x + 243*x^2 - 466*x^3 + 243*x^4 - 33*x^5 + x^6)/(1 - 52*x + 673*x^2 - 2548*x^3 + 3856*x^4 - 2548*x^5 + 673*x^6 - 52*x^7 + x^8). - Andrew Howroyd, Nov 14 2025

Mathematica

a[n_] := 2^n * Sqrt[Resultant[ChebyshevU[2*n, x/2], ChebyshevT[6, I*x/2], x]]; Array[a, 18, 0] (* Amiram Eldar, May 04 2021 *)

Prog

(PARI) {a(n) = sqrtint(4^n*polresultant(polchebyshev(2*n, 2, x/2), polchebyshev(6, 1, I*x/2)))}

Crossrefs

Column 3 of A103997.

Column 6 of A334178.

Sequence in context: A035277 A011906 A255859 * A183498 A254381 A177098

Adjacent sequences: A334176 A334177 A334178 * A334180 A334181 A334182

Keyword

nonn,easy

Author

Seiichi Manyama, Apr 17 2020

Status

approved