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%I #25 Sep 08 2022 08:45:06
%S 0,2,5,8,9,4,-15,-64,-175,-412,-903,-1904,-3927,-7996,-16159,-32512,
%T -65247,-130748,-261783,-523888,-1048135,-2096668,-4193775,-8388032,
%U -16776591,-33553756,-67108135,-134216944,-268434615,-536870012,-1073740863,-2147482624,-4294966207,-8589933436,-17179867959
%N a(n) = (n-1)*(n+3) - 2^n + 4.
%D J. Propp, Enumeration of matchings: problems and progress, pp. 255-291 in L. J. Billera et al., eds, New Perspectives in Algebraic Combinatorics, Cambridge, 1999 (see Problem 12).
%H Vincenzo Librandi, <a href="/A071099/b071099.txt">Table of n, a(n) for n = 0..1000</a>
%H J. Propp, <a href="http://faculty.uml.edu/jpropp/update.pdf">Updated article</a>
%H J. Propp, Enumeration of matchings: problems and progress, in L. J. Billera et al. (eds.), <a href="http://www.msri.org/publications/books/Book38/contents.html">New Perspectives in Algebraic Combinatorics</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (5,-9,7,-2).
%F G.f.: x*(2 - 5*x + x^2)/((1-x)^3*(1-2*x)). - _Colin Barker_, May 10 2012
%F a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4). - _Vincenzo Librandi_, May 11 2012
%e G.f. = 2*x + 5*X^2 + 8*X^3 + 9*X^4 + 4*X^5 - 15*X^6 - 64*X^7 - 175*X^8 + ...
%t Table[(2*n^2-2^n)/2,{n,5!}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 26 2010 *)
%t CoefficientList[Series[x*(2-5*x+x^2)/((1-x)^3*(1-2*x)),{x,0,40}],x] (* _Vincenzo Librandi_, May 11 2012 *)
%t LinearRecurrence[{5,-9,7,-2},{0,2,5,8},40] (* _Harvey P. Dale_, Jan 14 2015 *)
%o (Magma) [(n-1)*(n+3)-2^n+4: n in [0..40]]; // _Vincenzo Librandi_, May 11 2012
%K sign,easy
%O 0,2
%A _N. J. A. Sloane_, May 28 2002
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