

A103517


Expansion of (1+2*xx^2)/(1x)^2.


9



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
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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(nk))*(n+1).
Equals binomial transform of [1, 3, 1, 1, 1, 1, ...].  Gary W. Adamson, Apr 23 2008
a(n) = 2*a(n1)  a(n2) 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

with(numtheory):seq(ceil(mcombine(n, 2*n, 3*n, 4*n)/2), n=1..63); # Zerinvary Lajos, Apr 11 2008


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
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



