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A027561

Number of 4-unbalanced strings of length n (=2^n-A027559(n)).

0, 0, 0, 0, 0, 2, 6, 22, 56, 152, 356, 858, 1914, 4334, 9372, 20440, 43280, 92114, 192182, 402246, 830328, 1717496, 3517668, 7214218, 14689994, 29938526, 60697148, 123127224, 248807472, 502963778, 1013829414, 2044098166

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OFFSET

0,6

COMMENTS

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

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,2,-11,3,6).

FORMULA

For n>0, a(n) = 2*Fibonacci(n+3) + 2^n + [5(-1)^n - 19]*3^[n/2-1]. - Ralf Stephan, May 13 2004

G.f.: 2*x^5/((1-2*x)*(1-x-x^2)*(1-3*x^2)). [Colin Barker, Sep 20 2012]

MATHEMATICA

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 *)

LinearRecurrence[{3, 2, -11, 3, 6}, {0, 0, 0, 0, 0, 2}, 40] (* Harvey P. Dale, Oct 12 2019 *)

CROSSREFS

Cf. A027559.

Sequence in context: A212872 A306967 A324913 * A321626 A126171 A228396