|
Search: id:A102090
|
|
|
| A102090 |
|
Number of matchings in the C_n X P_3 graph (C_n is the cycle graph on n vertices and P_3 is the path graph on 3 vertices). |
|
+0
2
|
|
| 47, 228, 1511, 9213, 57536, 356863, 2217871, 13775700, 85579087, 531616825, 3302453192, 20515048427, 127440964999, 791672146068, 4917923140383, 30550483740725, 189781751728736, 1178937572877255, 7323643025265351
(list; graph; listen)
|
|
|
OFFSET
|
2,1
|
|
|
COMMENT
|
Row sums of A102089.
|
|
REFERENCES
|
H. Hosoya and A. Motoyama, An effective algorithm for obtaining polynomials for dimer statistics. Application of operator technique on the topological index to two- and three-dimensional rectangular and torus lattices, J. Math. Physics 26 (1985) 157-167 (eq. (52) and Table VII).
|
|
FORMULA
|
a(n)=3a(n-1)+19a(n-2)+10a(n-3)-24a(n-4)-10a(n-5)+11a(n-6)+a(n-7)-a(n-8) with a(2)=47, a(3)=228, a(4)=1511, a(5)=9213, a(6)=57536, a(7)=356863, a(8)=2217871, and a(9)=13775700. G.f.=-z^2*(-47-87z+66z^2+122z^3-36z^4-40z^5+5z^6+3z^7)/[(z^2-1-z)(z+1)(z^5-z^4-9z^3+9z^2+5z-1)].
|
|
MAPLE
|
a[2]:=47: a[3]:=228: a[4]:=1511: a[5]:=9213: a[6]:=57536: a[7]:=356863: a[8]:=2217871: a[9]:=13775700: for n from 10 to 23 do a[n]:=3*a[n-1]+19*a[n-2]+10*a[n-3]-24*a[n-4]-10*a[n-5]+11*a[n-6]+a[n-7]-a[n-8] od:seq(a[n], n=2..23);
|
|
CROSSREFS
|
Cf. A102089.
Adjacent sequences: A102087 A102088 A102089 this_sequence A102091 A102092 A102093
Sequence in context: A142203 A067986 A141537 this_sequence A033226 A142946 A142084
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 29 2004
|
|
|
Search completed in 0.005 seconds
|
