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a(n) = 2^(n-2)*(n-2)^2+2^(n-1).
1

%I #26 Sep 08 2022 08:46:04

%S 2,6,24,88,288,864,2432,6528,16896,42496,104448,251904,598016,1400832,

%T 3244032,7438336,16908288,38141952,85458944,190316544,421527552,

%U 929038336,2038431744,4454350848,9697230848,21038628864,45499809792,98113159168,210990268416

%N a(n) = 2^(n-2)*(n-2)^2+2^(n-1).

%H Vincenzo Librandi, <a href="/A217527/b217527.txt">Table of n, a(n) for n = 2..1000</a>

%H W. Griffiths, R. Smith and D. Warren, <a href="http://www.mat.unisi.it/newsito/puma/public_html/22_2/griffiths_smith_warren.pdf">Almost avoiding pairs of permutations</a>, PU. M. A. Vol. 22 (2011), 129-139.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-12,8).

%F a(n) = 6*a(n-1)-12*a(n-2)+8*a(n-3). G.f.: -2*x^2*(6*x^2-3*x+1)/(2*x-1)^3. [_Colin Barker_, Oct 17 2012]

%t Table[2^(n-2) (n-2)^2 + 2^(n-1), {n, 2, 30}] (* _Vincenzo Librandi_, Mar 11 2013 *)

%o (Maxima) makelist(2^(n-2)*(n-2)^2+2^(n-1), n, 2, 30); /* _Martin Ettl_, Oct 15 2012 */

%o (Magma) [2^(n-2)*(n-2)^2+2^(n-1): n in [2..30]]; // _Vincenzo Librandi_, Mar 11 2013

%K nonn,easy

%O 2,1

%A _N. J. A. Sloane_, Oct 13 2012