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 A030236 Cycle-path coverings of a family of digraphs. 1
 1, 2, 7, 18, 49, 136, 377, 1044, 2891, 8006, 22171, 61398, 170029, 470860, 1303949, 3611016, 9999959, 27692810, 76689487, 212375610, 588130153, 1628704336, 4510358465, 12490501212, 34589849507, 95789405774, 265268869027 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES O. M. D'Antona and E. Munarini, The Cycle-path Indicator Polynomial of a Digraph, Advances in Applied Mathematics 25 (2000), 41-56. LINKS FORMULA a(n+4) = 3 a(n+3) - a(n+2) + a(n+1), n >= 0. a(n+3) = 2*a(n+2) + a(n+1) + 2*sum( a(i), i = 0..n ), n >= 0. G.f.: (1-x+2*x^2-2*x^3)/(1-3*x+x^2-x^3). a(n) = sum(binomial(n+k+1,3*k+1)*2^k,k=0..n)+2*sum(binomial(n+k-1,3*k+1)*2^k,k=0..n-1). [Emanuele Munarini, Dec 03 2012] PROG (Maxima) makelist(sum(binomial(n+k+1, 3*k+1)*2^k, k, 0, n)+2*sum(binomial(n+k-1, 3*k+1)*2^k, k, 0, n-1), n, 0, 60); [Emanuele Munarini, Dec 03 2012] CROSSREFS Cf. A030186. Sequence in context: A022726 A192873 A017925 * A074141 A122931 A094976 Adjacent sequences:  A030233 A030234 A030235 * A030237 A030238 A030239 KEYWORD nonn,easy AUTHOR Ottavio D'Antona (dantona(AT)dsi.unimi.it) and Emanuele Munarini. STATUS approved

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Last modified April 25 18:12 EDT 2019. Contains 322461 sequences. (Running on oeis4.)