pillarman.js

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 range = n => Array(n).fill().map((_, i) => i);
const coverNegative = f => n => n < 0 ? 0 : f(n);
const conjugatePair = (a, b) => [a+b, a-b];

const a = coverNegative(
  n => 4*b(n-1) + 2*a(n-1) + a(n-2) + iverson(0)(n)
);

const b = coverNegative(
  n => a(n-1) + b(n-1)
); 

const [alpha, beta] = conjugatePair(1, Math.sqrt(3));

const A = 1/3;
const [B, C] = conjugatePair(1/3, 1/(2*Math.sqrt(3)));

const soln = n => A*(-1)**n + B*alpha**n + C*beta**n;

console.log(
  range(10).map(a)
);

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