A334135 Number of dimer tilings of a 2*n x 4 Moebius strip.

1, 7, 71, 769, 8449, 93127, 1027207, 11332097, 125019649, 1379271559, 15216755911, 167878292737, 1852111179521, 20433349871431, 225430197438727, 2487050546734081, 27438295728380929, 302712011022644999, 3339659377008916807, 36844671993005504257, 406487518942362537217

Offset: 0

Author

Seiichi Manyama, Apr 15 2020

Keywords

• nonn
• easy

Links

• Wikipedia, Chebyshev polynomials
• Wikipedia, Resultant
• Index entries for linear recurrences with constant coefficients, signature (14,-34,14,-1).

Crossrefs

Column 2 of A103997.

Programs

Mathematica

a[n_] := 2^n * Sqrt[Resultant[ChebyshevU[2*n, x/2], ChebyshevT[4, I*x/2], x]]; Array[a, 21, 0] (* Amiram Eldar, May 04 2021 *)

PARI

a(n) = sqrtint(4^n*polresultant(polchebyshev(2*n, 2, x/2), 1+2*x^2+1/2*x^4))

PARI

N=20; x='x+O('x^N); Vec(((1-x)*(1-6*x+x^2))/(1-14*x+34*x^2-14*x^3+x^4))

Formula

a(n)^2 = 4^n * Resultant(U(2*n,x), 1+2*x^2+1/2*x^4), where U(n,x) is a Chebyshev polynomial of the second kind and i = sqrt(-1).

G.f.: ((1-x)*(1-6*x+x^2))/(1-14*x+34*x^2-14*x^3+x^4).

a(n) = 14*a(n-1) - 34*a(n-2) + 14*a(n-3) - a(n-4) for n > 3.