A027556 Unbalanced strings of length n.

0, 0, 0, 2, 6, 18, 42, 98, 210, 450, 930, 1922, 3906, 7938, 16002, 32258, 64770, 130050, 260610, 522242, 1045506, 2093058, 4188162, 8380418, 16764930, 33538050, 67084290, 134184962, 268386306, 536805378, 1073643522

Offset: 0

Author

R. K. Guy, David Callan

Keywords

• nonn
• easy

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 triangle with side length one. E.g., mark the vertices of the triangle as 1, 2 and 3. Having a yardstick with n = 3 sticks there are two ways of folding to form an equilateral triangle: 1-2-3-1 and 1-3-2-1. For n = 4 there are six ways of folding: 1-2-3-1-2 or 3; 1-3-2-1-2 or 3; 1-2-1-3-2 and 1-3-1-2-3. - Frank Hollstein, Apr 23 2019

Links

• Index entries for linear recurrences with constant coefficients, signature (3,0,-6,4).

Crossrefs

Cf. A000079 (2^n), A027383.

Formula

a(n) = 2^n - A027383(n).

G.f.: 2*x^2/((1-x)*(1-2*x)(1-2*x^2)).