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A102090
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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).
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1
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47, 228, 1511, 9213, 57536, 356863, 2217871, 13775700, 85579087, 531616825, 3302453192, 20515048427, 127440964999, 791672146068, 4917923140383, 30550483740725, 189781751728736, 1178937572877255, 7323643025265351
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,1
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COMMENTS
| Row sums of A102089.
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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).
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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)].
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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);
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MATHEMATICA
| LinearRecurrence[{3, 19, 10, -24, -10, 11, 1, -1}, {47, 228, 1511, 9213, 57536, 356863, 2217871, 13775700}, 30] (* From Harvey P. Dale, Oct 24 2011 *)
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CROSSREFS
| Cf. A102089.
Sequence in context: A142203 A067986 A141537 * A033226 A142946 A204794
Adjacent sequences: A102087 A102088 A102089 * A102091 A102092 A102093
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 29 2004
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