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 A103517 Expansion of (1+2*x-x^2)/(1-x)^2. 10
 1, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Row sums of A103516. Also the number of maximal and maximum cliques in the (n+1) X (n+1) rook graph. - Eric W. Weisstein, Sep 14 2017 Also the number of maximal and maximum independent vertex sets in the (n+1) X (n+1) rook complement graph. - Eric W. Weisstein, Sep 14 2017 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Eric Weisstein's World of Mathematics, Maximal Clique Eric Weisstein's World of Mathematics, Maximum Clique Eric Weisstein's World of Mathematics, Maximal Independent Vertex Set Eric Weisstein's World of Mathematics, Maximum Independent Vertex Set Eric Weisstein's World of Mathematics, Rook Complement Graph Eric Weisstein's World of Mathematics, Rook Graph Index entries for linear recurrences with constant coefficients, signature (2,-1). FORMULA a(n) = 2*n + 2 - 0^n. a(n) = Sum_{k=0..n} 0^(k(n-k))*(n+1). Equals binomial transform of [1, 3, -1, 1, -1, 1, ...]. - Gary W. Adamson, Apr 23 2008 a(n) = 2*a(n-1) - a(n-2) for n > 2. - Eric W. Weisstein, Sep 14 2017 G.f.: (1 + 2*x - x^2)/(-1 + x)^2. - Eric W. Weisstein, Sep 14 2017 MAPLE a := n -> 2*(n + 1) - 0^n: seq(a(n), n = 0..62); # Peter Luschny, May 12 2023 MATHEMATICA CoefficientList[Series[(-z^2 + 2*z + 1)/(z - 1)^2, {z, 0, 100}], z] (* Vladimir Joseph Stephan Orlovsky, Jul 10 2011 *) CoefficientList[Series[2/(x - 1)^2 - 1, {x, 0, 62}], x] (* Robert G. Wilson v, Jan 29 2015 *) Join[{1}, 2 Range[2, 20]] (* Eric W. Weisstein, Sep 14 2017 *) Join[{1}, LinearRecurrence[{2, -1}, {4, 6}, 20]] (* Eric W. Weisstein, Sep 14 2017 *) PROG (Magma) [1] cat [2*n+2 : n in [1..60]]; // Wesley Ivan Hurt, Dec 07 2016 CROSSREFS Cf. A103516. Essentially the same as A004277, A005843, A051755, and A076032. - R. J. Mathar, Jul 31 2010 Cf. A272651 (for which this sequence is a conjectured continuation for large n). Sequence in context: A175074 A063127 A272651 * A163300 A193175 A093161 Adjacent sequences: A103514 A103515 A103516 * A103518 A103519 A103520 KEYWORD easy,nonn AUTHOR Paul Barry, Feb 09 2005 STATUS approved

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Last modified April 24 17:29 EDT 2024. Contains 371962 sequences. (Running on oeis4.)