spiral.js

var target = 368078;

var size = 20;
var arr = new Array(size);
for (var i = 0; i < size; i++) {
    arr[i] = new Array(size);
    arr[i].fill(0);
}

var offset

var zeroOffset = Math.floor(size / 2);

arr[zeroOffset][zeroOffset] = 1;

var hrstart = process.hrtime();;

var side = 0;
var posInSide = 0;
var posInLayer = 0;
var layer = 0;
var nextLayer = 2;
var sideLength = 1;
var val = 1;
var nextSide = 2;
var i;
for (i = 2; val <= target && i < (size - 2) * (size - 2); i++, posInSide++) {
    if (i == nextLayer) {
        layer++;
        sideLength += 2;
        nextLayer = sideLength * sideLength + 1;
        posInLayer = 0;
        side = -1;
    }
    if (i == nextSide) {
        nextSide = i + (sideLength - 1);
        posInSide = 0;
        side++;
    }

    var coords = {x: zeroOffset, y: zeroOffset};
    var mul = (side > 1) ? -1 : 1;
    var dir = (side & 1);
    var offset = (posInSide - (sideLength - 3) / 2);

    if (dir == 0) {
        coords.x += mul * layer;
        coords.y += mul * offset;
    } else {
        coords.x -= mul * offset;
        coords.y += mul * layer;
    }

    val = 0;
    val += arr[coords.y + 1][coords.x + 1];
    val += arr[coords.y + 1][coords.x    ];
    val += arr[coords.y + 1][coords.x - 1];
    val += arr[coords.y    ][coords.x - 1];
//  val += arr[coords.y    ][coords.x    ];
    val += arr[coords.y    ][coords.x + 1];
    val += arr[coords.y - 1][coords.x - 1];
    val += arr[coords.y - 1][coords.x    ];
    val += arr[coords.y - 1][coords.x + 1];

    arr[coords.y][coords.x] = val;
}

hrend = process.hrtime(hrstart);
console.log(val);
console.log("Execution time: %ds", hrend[0] + hrend[1]/1e9);