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Expansion of x*(3*x^2+x+1)/((x-1)*(2*x-1)*(x+1)).
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%I #25 Mar 23 2018 16:35:08

%S 0,1,3,10,21,46,93,190,381,766,1533,3070,6141,12286,24573,49150,98301,

%T 196606,393213,786430,1572861,3145726,6291453,12582910,25165821,

%U 50331646,100663293,201326590,402653181,805306366,1610612733,3221225470,6442450941,12884901886

%N Expansion of x*(3*x^2+x+1)/((x-1)*(2*x-1)*(x+1)).

%C a(n) is the number of edges of the shuffle-exchange graph SE_n with self-loops removed.

%H Alois P. Heinz, <a href="/A192033/b192033.txt">Table of n, a(n) for n = 0..1000</a>

%H D. Kleitman, F. T. Leighton, M. Lepley, and G. L. Miller, <a href="http://doi.acm.org/10.1145/800076.802480">New layouts for the shuffle-exchange graph (Extended Abstract)</a>, Proceedings of the 13th annual ACM symposium on Theory of Computing (STOC '81), 1981, 278-292.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Shuffle-ExchangeGraph.html">Shuffle-Exchange Graph</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-2).

%F G.f.: x*(3*x^2+x+1)/((x-1)*(2*x-1)*(x+1)).

%F a(n) = 3*2^(n-1) -3 + (n mod 2) for n>0, a(0) = 0.

%p a:= n-> `if`(n=0, 0, 3*2^(n-1) -3 +irem(n, 2)):

%p seq(a(n), n=0..40);

%t LinearRecurrence[{2,1,-2},{0,1,3,10},40] (* _Harvey P. Dale_, Mar 23 2018 *)

%Y Cf. A240802.

%K nonn,easy

%O 0,3

%A _Alois P. Heinz_, May 06 2012