Vue pagination with limit

Hello guys,

I created a pagination component, this pagination has links limit just like Laravel pagination. Currently everything seems to be working fine but I had doubt since I'm not good in math, please review my code especially on links computed data. Here is my code:

<nav v-if="show">
    <ul class="pagination">
        <li :class="{ disabled: ! prev }" v-on:click="go(prev)"><span>&laquo;</span></li>
        <li v-for="link in links" track-by="$index" :class="{ active: current == link, disabled: isNaN(link) }" v-on:click="go(link)"><span>{{ link }}</span></li>
        <li :class="{ disabled: ! next }" v-on:click="go(next)"><span>&raquo;</span></li>
    </ul>
</nav>

Vue.component('pagination', {
    template: '#pagination',
    props: {
        total: {
            type: Number,
            default: 0
        },
        current: {
            type: Number,
            default: 1
        },
        limit: {
            type: Number,
            default: 4,
            coerce: function (limit) {
                return limit - 1;
            }
        }
    },
    data: function () {
        return {
            show: false
        };
    },
    computed: {
        pages: function () {
            var pages = [];

            for (var i = 1; i <= this.total; i++) {
                pages.push(i);
            }

            return pages;
        },
        links: function () {
            var first = [1, '...'],
                last = ['...', this.total],
                range = [];

            if (this.current <= this.limit) {
                range = this.range(1, this.limit + 1);

                return (this.current + range.length) <= this.total ? range.concat(last) : range;
            } else if (this.current > (this.total - this.limit)) {
                range = this.range(this.total - (this.limit), this.total);

                return (this.current - range.length) >= 1 ? first.concat(range) : range;
            } else {
                range = this.range(this.current - Math.ceil(this.limit / 2), this.current + Math.ceil(this.limit / 2));

                return first.concat(range).concat(last);
            }
        },
        next: function () {
            var next = this.current + 1;

            return next <= this.total ? next : false;
        },
        prev: function () {
            return this.current - 1;
        },
        show: function () {
            return this.next || this.prev;
        }
    },
    methods: {
        range: function (start, end) {
            var pages = [];

            for (var i = start - 1; i < end; i++) {
                if (this.pages[i]) {
                    pages.push(this.pages[i]);
                }
            }

            return pages;
        },
        go: function (page) {
            if (isNaN(page)) {
                return;
            }
            
            this.$dispatch('paginate:to', page);
        }
    }
});

And here is live fiddle to see how it works: https://jsfiddle.net/reefki/402tLv3n/