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A334180 Number of dimer tilings of a 2*n x 8 Moebius strip. 2
1, 47, 4271, 434657, 46069729, 4974089647, 541714928431, 59235304882177, 6489376893239297, 711542422708907311, 78049793235712789423, 8562932336475599244257, 939528644055272842890721, 103089508033934831216777903, 11311669427350891385087911471 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..14.

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: A005148 A123798 A104069 * A194617 A217229 A217230

Adjacent sequences:  A334177 A334178 A334179 * A334181 A334182 A334183

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Apr 17 2020

STATUS

approved

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Last modified May 25 21:44 EDT 2022. Contains 354071 sequences. (Running on oeis4.)