A103997
Square array T(M,N) read by antidiagonals: number of dimer tilings of a 2*M X 2*N Moebius strip.
Original entry on oeis.org
1, 1, 1, 1, 3, 1, 1, 11, 7, 1, 1, 41, 71, 18, 1, 1, 153, 769, 539, 47, 1, 1, 571, 8449, 17753, 4271, 123, 1, 1, 2131, 93127, 603126, 434657, 34276, 322, 1, 1, 7953, 1027207, 20721019, 46069729, 10894561, 276119, 843, 1, 1, 29681, 11332097, 714790675, 4974089647, 3625549353, 275770321, 2226851, 2207, 1
Offset: 0
Array begins:
1, 1, 1, 1, 1, 1, 1,
1, 3, 7, 18, 47, 123, 322,
1, 11, 71, 539, 4271, 34276, 276119,
1, 41, 769, 17753, 434657, 10894561, 275770321,
1, 153, 8449, 603126, 46069729, 3625549353, 289625349454,
1, 571, 93127, 20721019, 4974089647, 1234496016491, 312007855309063,
...
- Laura Florescu, Daniela Morar, David Perkinson, Nicholas Salter and Tianyuan Xu, Sandpiles and Dominos, El. J. Comb., 22 (2015), P1.66. See Theorem 18.
- W. T. Lu and F. Y. Wu, Dimer statistics on the Moebius strip and the Klein bottle, arXiv:cond-mat/9906154 [cond-mat.stat-mech], 1999.
- Index entries for sequences related to dominoes
-
T[M_, N_] := Product[4Sin[(4n-1)Pi/(4N)]^2 + 4Cos[m Pi/(2M+1)]^2, {n, 1, N}, {m, 1, M}];
Table[T[M - N, N] // Round, {M, 0, 9}, {N, 0, M}] // Flatten (* Jean-François Alcover, Dec 03 2018 *)
A334179
Number of dimer tilings of a 2*n x 6 Moebius strip.
Original entry on oeis.org
1, 18, 539, 17753, 603126, 20721019, 714790675, 24693540102, 853526336417, 29507528240963, 1020183543633762, 35272351950083641, 1219535200106522761, 42165342386915661378, 1457865351514568764211, 50405667966576581717969, 1742775306265709714234214, 60256436430143085819341347
Offset: 0
-
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 *)
-
{a(n) = sqrtint(4^n*polresultant(polchebyshev(2*n, 2, x/2), polchebyshev(6, 1, I*x/2)))}
A334180
Number of dimer tilings of a 2*n x 8 Moebius strip.
Original entry on oeis.org
1, 47, 4271, 434657, 46069729, 4974089647, 541714928431, 59235304882177, 6489376893239297, 711542422708907311, 78049793235712789423, 8562932336475599244257, 939528644055272842890721, 103089508033934831216777903, 11311669427350891385087911471
Offset: 0
-
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 *)
-
{a(n) = sqrtint(4^n*polresultant(polchebyshev(2*n, 2, x/2), polchebyshev(8, 1, I*x/2)))}
A334181
Number of dimer tilings of a 2*n x 10 Moebius strip.
Original entry on oeis.org
1, 123, 34276, 10894561, 3625549353, 1234496016491, 425588878897051, 147716667776449068, 51459452422736225401, 17962375573820654607091, 6276640725138515237851803, 2194525820018749279915303361, 767517569389298359121889024076, 268477550040900162034429991254323
Offset: 0
-
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 *)
-
{a(n) = sqrtint(4^n*polresultant(polchebyshev(2*n, 2, x/2), polchebyshev(10, 1, I*x/2)))}
A334182
Number of dimer tilings of a 2*n x 12 Moebius strip.
Original entry on oeis.org
1, 322, 276119, 275770321, 289625349454, 312007855309063, 341133743251787719, 376320092633385077198, 417378876015895466713681, 464421220758849403137304663, 517771128105959394949223994178, 577920313480485996169789045855489, 645503767039127463811947619425652481
Offset: 0
-
a[n_] := 2^n * Sqrt[Resultant[ChebyshevU[2*n, x/2], ChebyshevT[12, I*x/2], x]]; Array[a, 13, 0] (* Amiram Eldar, May 04 2021 *)
-
{a(n) = sqrtint(4^n*polresultant(polchebyshev(2*n, 2, x/2), polchebyshev(12, 1, I*x/2)))}
A334183
Number of dimer tilings of a 2*n x 14 Moebius strip.
Original entry on oeis.org
1, 843, 2226851, 7009284232, 23313951730593, 79684937704014787, 276820366633357961907, 971684488369988888850993, 3433809783046699326165318697, 12187832583695135440208385490411, 43381711462091769247169214041784216, 154696550169813236996441805153918153313
Offset: 0
-
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 *)
-
{a(n) = sqrtint(4^n*polresultant(polchebyshev(2*n, 2, x/2), polchebyshev(14, 1, I*x/2)))}
Showing 1-6 of 6 results.