A263201 - OEIS

%I #18 Nov 06 2015 14:35:39

%S 11,37,71,252,539,1813,4271,13519,34276,103803,276119,813417,2226851,

%T 6455052,17965151,51604017,144948419,414258603,1169523076,3333192319,

%U 9436433171,26853404413,76139155439,216490730652,614339685971,1745997031837,4956888901511

%N Number of perfect matchings on a Möbius strip of width 4 and length n.

%C This sequence obeys the same recurrence relation as A252054.

%H Colin Barker, <a href="/A263201/b263201.txt">Table of n, a(n) for n = 2..1000</a>

%H W. T. Lu and F. Y. Wu, <a href="http://dx.doi.org/10.1016/S0375-9601(02)00019-1">Close-packed dimers on nonorientable surfaces</a>, Physics Letters A, 293(2002), 235-246.

%H S. N. Perepechko, <a href="http://www.cmmass.ru/files/cmmass2015_web.pdf">Recurrence relations for the number of perfect matchings on the Mobius strips (in Russian)</a>, Proc. of XIX international conference on computational mechanics and modern applied software systems (CMMASS'2015), Alushta, Crimea, 2015, 98-100.

%H Sergey Perepechko, <a href="/A263201/a263201.png">Graph view</a>

%H G. Tesler, <a href="http://dx.doi.org/10.1006/jctb.1999.1941">Matchings in graphs on non-orientable surfaces</a>, Journal of Combinatorial Theory B, 78(2000), 198-231.

%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (1,13,-7,-61,12,128,0,-128,-12,61,7,-13,-1,1).

%F G.f.: z^2*(11 + 26*z - 109*z^2 - 223*z^3 + 294*z^4 + 620*z^5 - 306*z^6 -764*z^7 + 100*z^8 + 414*z^9 + 5*z^10 - 92*z^11 - 3*z^12 + 7*z^13)/((1 - z)*(1 + z)*(1 + z - 3*z^2 - z^3 + z^4)*(1 - z - 3*z^2 + z^3 + z^4)*(1 - z - 5*z^2 - z^3 + z^4)).

%t CoefficientList[Series[(11 + 26 x - 109 x^2 - 223 x^3 + 294 x^4 + 620 x^5 - 306 x^6 - 764 x^7 + 100 x^8 + 414 x^9 + 5 x^10 - 92 x^11 - 3 x^12 + 7 x^13)/((1 - x) (1 + x) (1 + x - 3 x^2 - x^3 + x^4) (1 - x - 3 x^2 + x^3 + x^4) (1 - x - 5 x^2 - x^3 + x^4)), {x, 0, 33}], x] (* _Vincenzo Librandi_, Oct 12 2015 *)

%o (PARI) Vec(z^2*(11 + 26*z - 109*z^2 - 223*z^3 + 294*z^4 + 620*z^5 - 306*z^6 -764*z^7 + 100*z^8 + 414*z^9 + 5*z^10 - 92*z^11 - 3*z^12 + 7*z^13)/((1 - z)*(1 + z)*(1 + z - 3*z^2 - z^3 + z^4)*(1 - z - 3*z^2 + z^3 + z^4)*(1 - z - 5*z^2 - z^3 + z^4)) + O(z^50)) \\ _Altug Alkan_, Oct 12 2015

%Y Cf. A020878, A263200.

%K nonn

%O 2,1

%A _Sergey Perepechko_, Oct 12 2015