freeCodeCamp/curriculum/challenges/english/08-coding-interview-prep/project-euler/problem-435-polynomials-of-fibonacci-numbers.english.md

id, challengeType, title

id	challengeType	title
5900f5201000cf542c510032	5	Problem 435: Polynomials of Fibonacci numbers

Description

The Fibonacci numbers {fn, n ≥ 0} are defined recursively as fn = fn-1 + fn-2 with base cases f0 = 0 and f1 = 1. Define the polynomials {Fn, n ≥ 0} as Fn(x) = ∑fixi for 0 ≤ i ≤ n. For example, F7(x) = x + x2 + 2x3 + 3x4 + 5x5 + 8x6 + 13x7, and F7(11) = 268357683. Let n = 1015. Find the sum [∑0≤x≤100 Fn(x)] mod 1307674368000 (= 15!).

Instructions

Tests

tests:
  - text: <code>euler435()</code> should return 252541322550.
    testString: assert.strictEqual(euler435(), 252541322550);

Challenge Seed

function euler435() {
  // Good luck!
  return true;
}

euler435();

Solution

// solution required