Scratchpad for problem 4

Convolve.js

const fact = n => n <= 0 ? 1 : n * fact(n-1);
const choose = (n, k) => fact(n) / (fact(n - k) * fact(k));
const mapper = predicate => n => predicate(n) ? 1 : 0;
const [isEven, isOdd] = [0,1].map(k => mapper(n => n % 2 === k));
const iverson = k => mapper(n => n === k);
const coverNegative = f => n => n < 0 ? 0 : f(n);
const conjugatePair = (a, b) => [a+b, a-b];
const round = fn => n => Math.round(fn(n));
const range = n => Array(n).fill().map((_, i) => i);
const reversed = xs => [...xs].reverse();
const zip = (...xss) => (
  len => range(len).map(
    idx => xss.reduce(
      (acc, xs) => [...acc, xs[idx]],
      []
    )
  )
)(Math.min(...xss.map(({ length }) => length)));
const convolve = (A, B) => zip(A, reversed(B)).reduce(
  (acc, [a, b]) => acc + a*b,
  0,
);
const b_ = n => n === 0
  ? 1
  : (
    last => convolve(last, last)
  )(range(n).map(b_));
const soln = n => ( 1 / (n + 1)) * choose(2*n, n);

console.log(
  range(10).map(b_),
  range(10).map(soln),
);