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A334181 Number of dimer tilings of a 2*n x 10 Moebius strip. 2
1, 123, 34276, 10894561, 3625549353, 1234496016491, 425588878897051, 147716667776449068, 51459452422736225401, 17962375573820654607091, 6276640725138515237851803, 2194525820018749279915303361, 767517569389298359121889024076, 268477550040900162034429991254323 (list; graph; refs; listen; history; text; internal format)
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: A049670 A181006 A289331 * A033522 A214464 A288353

Adjacent sequences:  A334178 A334179 A334180 * A334182 A334183 A334184

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Apr 17 2020

STATUS

approved

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Last modified June 30 09:38 EDT 2022. Contains 354920 sequences. (Running on oeis4.)