|
| |
|
|
A028447
|
|
Number of perfect matchings in graph P_{2} X P_{3} X P_{n}.
|
|
2
|
|
|
|
1, 3, 32, 229, 1845, 14320, 112485, 880163, 6895792, 54003765, 422983905, 3312866080, 25947198337, 203223953179, 1591695681488, 12466511517581, 97640484615909, 764741896529104, 5989627994067061, 46912093390144139, 367425909133064576, 2877761124002870925
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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
|
| |
|
|
