A028447 Number of perfect matchings in graph P_{2} X P_{3} X P_{n}.

1, 3, 32, 229, 1845, 14320, 112485, 880163, 6895792, 54003765, 422983905, 3312866080, 25947198337, 203223953179, 1591695681488, 12466511517581, 97640484615909, 764741896529104, 5989627994067061, 46912093390144139, 367425909133064576, 2877761124002870925

Offset

0,2

Comments

lim(a(n)^(1/n), n -> infinity) = 7.832221... - Emeric Deutsch, Oct 14 2006

Links

Table of n, a(n) for n=0..21.

Per Hakan Lundow, Computation of matching polynomials and the number of 1-factors in polygraphs, Research report, No 12, 1996, Department of Math., Umea University, Sweden.

Per Hakan Lundow, Enumeration of matchings in polygraphs, 1998.

R. J. Mathar, Tilings of rectangular regions by rectangular tiles: Counts derived from transfer matrices, arXiv:1406.7788 (2014), eq. (37).

H. Narumi and H. Hosoya, Generalized expression of the perfect matching number of 2 X 3 X n lattices, J. Math. Phys. 34 (3), 1993, 1043-1051.

Formula

a(n) = 6a(n - 1) + 21a(n - 2) - 42a(n - 3) - 89a(n - 4) + 68a(n - 5) + 89a(n - 6) - 42a(n - 7) - 21a(n - 8) + 6a(n - 9) + a(n - 10). - Emeric Deutsch, Oct 14 2006

G.f.: ( -1 +3*x +7*x^2 -16*x^3 -14*x^4 +16*x^5 +7*x^6 -3*x^7 -x^8 ) / ( (x^2-x-1) *(x^8 +7*x^7 -13*x^6 -48*x^5 +28*x^4 +48*x^3 -13*x^2 -7*x+1) ). - R. J. Mathar, Dec 06 2013

Maple

a[0]:=1: a[1]:=3: a[2]:=32: a[3]:=229: a[4]:=1845: a[5]:=14320: a[6]:=112485: a[7]:=880163: a[8]:=6895792: a[9]:=54003765: a[10]:=422983905: for n from 11 to 20 do a[n]:=6*a[n-1]+21*a[n-2]-42*a[n-3]-89*a[n-4]+68*a[n-5]+89*a[n-6]-42*a[n-7]-21*a[n-8]+6*a[n-9]+a[n-10] od: seq(a[n], n=0..30); # Emeric Deutsch, Oct 14 2006

Crossrefs

Column k=3 of A181206.

Sequence in context: A322234 A264574 A002059 * A081012 A187919 A198320

Adjacent sequences: A028444 A028445 A028446 * A028448 A028449 A028450

Keyword

nonn

Author

Per H. Lundow

Status

approved