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A027556
Unbalanced strings of length n.
1
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
0,4
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
FORMULA
a(n) = 2^n - A027383(n).
G.f.: 2*x^2/((1-x)*(1-2*x)(1-2*x^2)).
CROSSREFS
Cf. A000079 (2^n), A027383.
Sequence in context: A014741 A016059 A291519 * A195584 A225316 A272934
KEYWORD
nonn,easy
STATUS
approved