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 A163250 The number of nonisomorphic complete simple games with n voters of two different types. 2
 0, 0, 1, 5, 15, 36, 76, 148, 273, 485, 839, 1424, 2384, 3952, 6505, 10653, 17383, 28292, 45964, 74580, 120905, 195885, 317231, 513600, 831360, 1345536, 2177521, 3523733, 5701983, 9226500, 14929324, 24156724, 39087009, 63244757, 102332855 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Given on p. 2 of Freixas, and proved as Theorem 3.2. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Josep Freixas, Xavier Molinero, Salvador Roura, A Fibonacci sequence for linear structures with two types of components, arXiv:0907.3853 [math.CO], July 22, 2009. Index entries for linear recurrences with constant coefficients, signature (4,-5,1,2,-1). FORMULA a(n) = F(n+6) - (n^2 + 4*n + 8), where F(n) are the Fibonacci numbers. From R. J. Mathar, Jul 27 2009: (Start) a(n) = 4*a(n-1) -5*a(n-2) +a(n-3) +2*a(n-4) -a(n-5). G.f.: x^2*(1+x)/((1-x-x^2)*(1-x)^3). (End) a(n) = Sum_{k=0..n-1} Sum_{i=0..n-1} i^2 * C(n-k-1,k-i). - Wesley Ivan Hurt, Sep 21 2017 a(n) = A053808(n-2) for n >= 2. - Georg Fischer, Oct 28 2018 MAPLE with(numtheory): seq(coeff(series(x^2*(1+x)/((x^2+x-1)*(x-1)^3), x, n+1), x, n), n = 0 .. 40); # Muniru A Asiru, Oct 28 2018 MATHEMATICA LinearRecurrence[{4, -5, 1, 2, -1}, {0, 0, 1, 5, 15}, 40] (* or *) Table[ Fibonacci[n+6] -(n^2+4*n+8), {n, 0, 40}] (* G. C. Greubel, Dec 12 2016 *) PROG (PARI) concat([0, 0], Vec(x^2*(1+x)/((1-x-x^2)*(1-x)^3) + O(x^40))) \\ G. C. Greubel, Dec 12 2016 (MAGMA) [Fibonacci(n+6)-(n^2+4*n+8): n in [0..40]]; // Vincenzo Librandi, Sep 22 2017 (GAP) List([0..35], n->Fibonacci(n+6)-(n^2+4*n+8)); # Muniru A Asiru, Oct 28 2018 (Sage) f=fibonacci; [f(n+6) -(n^2+4*n+8) for n in (0..40)] # G. C. Greubel, Jul 06 2019 CROSSREFS Cf. A000045, A053808. Sequence in context: A086716 A046776 A144898 * A053808 A111926 A137609 Adjacent sequences:  A163247 A163248 A163249 * A163251 A163252 A163253 KEYWORD easy,nonn,uned AUTHOR Jonathan Vos Post, Jul 23 2009 EXTENSIONS More terms from R. J. Mathar, Jul 27 2009 STATUS approved

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Last modified February 18 04:48 EST 2020. Contains 332011 sequences. (Running on oeis4.)