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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
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
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
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.)