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%I #32 Oct 12 2019 15:55:01
%S 0,0,0,0,0,2,6,22,56,152,356,858,1914,4334,9372,20440,43280,92114,
%T 192182,402246,830328,1717496,3517668,7214218,14689994,29938526,
%U 60697148,123127224,248807472,502963778,1013829414,2044098166
%N Number of 4-unbalanced strings of length n (=2^n-A027559(n)).
%C a(n) is also the number of different ways to fold down a folding yardstick with n sticks (stick length is one) to form an equilateral pentagon with side length one. - _Frank Hollstein_, May 01 2019
%H Vincenzo Librandi, <a href="/A027561/b027561.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,2,-11,3,6).
%F For n>0, a(n) = 2*Fibonacci(n+3) + 2^n + [5(-1)^n - 19]*3^[n/2-1]. - _Ralf Stephan_, May 13 2004
%F G.f.: 2*x^5/((1-2*x)*(1-x-x^2)*(1-3*x^2)). [_Colin Barker_, Sep 20 2012]
%t CoefficientList[Series[2 x^5/((1 - 2 x) (1 - x - x^2) (1 - 3 x^2)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Oct 18 2013 *)
%t LinearRecurrence[{3,2,-11,3,6},{0,0,0,0,0,2},40] (* _Harvey P. Dale_, Oct 12 2019 *)
%Y Cf. A027559.
%K nonn,easy
%O 0,6
%A _R. K. Guy_, _David Callan_