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id	title	challengeType	forumTopicId	dashedName
5900f4eb1000cf542c50fffd	Problem 382: Generating polygons	5	302046	problem-382-generating-polygons

--description--

A polygon is a flat shape consisting of straight line segments that are joined to form a closed chain or circuit. A polygon consists of at least three sides and does not self-intersect.

A set S of positive numbers is said to generate a polygon P if:

no two sides of P are the same length,
the length of every side of P is in S, and
S contains no other value.

For example:

The set {3, 4, 5} generates a polygon with sides 3, 4, and 5 (a triangle).

The set {6, 9, 11, 24} generates a polygon with sides 6, 9, 11, and 24 (a quadrilateral).

The sets {1, 2, 3} and {2, 3, 4, 9} do not generate any polygon at all.

Consider the sequence s, defined as follows:

s_1 = 1, s_2 = 2, s_3 = 3
s_n = s_{n - 1} + s_{n - 3} for n > 3.

Let U_n be the set \\{s_1, s_2, \ldots, s_n\\}. For example, U_{10} = \\{1, 2, 3, 4, 6, 9, 13, 19, 28, 41\\}.

Let f(n) be the number of subsets of U_n which generate at least one polygon.

For example, f(5) = 7, f(10) = 501 and f(25) = 18\\,635\\,853.

Find the last 9 digits of f({10}^{18}).

--hints--

generatingPolygons() should return 697003956.

assert.strictEqual(generatingPolygons(), 697003956);

--seed--

--seed-contents--

function generatingPolygons() {

  return true;
}

generatingPolygons();

--solutions--

// solution required

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