The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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). 3
 47, 228, 1511, 9213, 57536, 356863, 2217871, 13775700, 85579087, 531616825, 3302453192, 20515048427, 127440964999, 791672146068, 4917923140383, 30550483740725, 189781751728736, 1178937572877255, 7323643025265351 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS Row sums of A102089. LINKS G. C. Greubel, Table of n, a(n) for n = 2..1000 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). Index entries for linear recurrences with constant coefficients, signature (3,19,10,-24,-10,11,1,-1). FORMULA 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) 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.: x^2*(47+87*x-66*x^2-122*x^3+36*x^4+40*x^5-5*x^6-3*x^7)/((1+x)*(1+x-x^2)*(1-5*x-9*x^2+9*x^3+x^4-x^5)). 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); MATHEMATICA LinearRecurrence[{3, 19, 10, -24, -10, 11, 1, -1}, {47, 228, 1511, 9213, 57536, 356863, 2217871, 13775700}, 30] (* Harvey P. Dale, Oct 24 2011 *) PROG (PARI) my(x='x+O('x^30)); Vec(x^2*(47+87*x-66*x^2-122*x^3+36*x^4+40*x^5 -5*x^6-3*x^7)/((1+x)*(1+x-x^2)*(1-5*x-9*x^2+9*x^3+x^4-x^5))) \\ G. C. Greubel, Oct 27 2019 (Magma) R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( x^2*(47+87*x-66*x^2-122*x^3+36*x^4+40*x^5-5*x^6-3*x^7)/((1+x)*(1+x-x^2)*(1-5*x-9*x^2+9*x^3+x^4-x^5)) )); // G. C. Greubel, Oct 27 2019 (Sage) def A102090_list(prec): P. = PowerSeriesRing(ZZ, prec) return P(x^2*(47+87*x-66*x^2-122*x^3+36*x^4+40*x^5-5*x^6-3*x^7)/( (1+x)*(1+x-x^2)*(1-5*x-9*x^2+9*x^3+x^4-x^5))).list() A102090_list(30) # G. C. Greubel, Oct 27 2019 (GAP) a:=[47, 228, 1511, 9213, 57536, 356863, 2217871, 13775700];; for n in [9..30] 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; a; # G. C. Greubel, Oct 27 2019 CROSSREFS Column 3 of A287428. Cf. A102089. Sequence in context: A142203 A067986 A141537 * A033226 A142946 A204794 Adjacent sequences: A102087 A102088 A102089 * A102091 A102092 A102093 KEYWORD nonn AUTHOR Emeric Deutsch, Dec 29 2004 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 2 19:19 EST 2024. Contains 370498 sequences. (Running on oeis4.)