✨ feat: Draft for sequence and count.

Author: make-github-pseudonymous-again

package.json

@@ -75,9 +75,10 @@
   "bugs": {
     "url": "https://github.com/aureooms/js-set-partition/issues"
   },
-  "dependencies": {},
+  "dependencies": {
+    "@aureooms/js-itertools": "^4.1.0"
+  },
   "devDependencies": {
-    "@aureooms/js-itertools": "^4.1.0",
     "@babel/cli": "7.11.6",
     "@babel/core": "7.11.6",
     "@babel/preset-env": "7.11.5",

src/count.js

@@ -0,0 +1,6 @@
+import {nth} from '@aureooms/js-itertools';
+
+import sequence from './sequence';
+
+const count = (k) => nth(sequence(), k);
+export default count;

src/index.js

@@ -1,8 +1,12 @@
+import count from './count';
 import isPartition from './isPartition';
+import sequence from './sequence';
 
 /* eslint import/no-anonymous-default-export: [2, {"allowObject": true}] */
 export default {
+	count,
 	isPartition,
+	sequence,
 };
 
-export {isPartition};
+export {count, isPartition, sequence};

src/sequence.js

@@ -0,0 +1,16 @@
+export default function* sequence() {
+	yield 1n;
+	const a = [1n];
+	while (true) {
+		const n = a.length;
+		let current = a[n - 1];
+		yield current;
+		for (let i = 0; i < n; ++i) {
+			const next = current + a[i];
+			a[i] = current;
+			current = next;
+		}
+
+		a.push(current);
+	}
+}

test/src/count.js

@@ -0,0 +1,18 @@
+import test from 'ava';
+
+import {count} from '../../src';
+
+const macro = (t, k, Bk) => {
+	t.is(count(k), Bk);
+};
+
+macro.title = (title, k, Bk) => `count(${k}) = ${Bk}`;
+
+test(macro, 0, 1n);
+test(macro, 1, 1n);
+test(macro, 2, 2n);
+test(macro, 3, 5n);
+test(macro, 4, 15n);
+test(macro, 5, 52n);
+test(macro, 6, 203n);
+test(macro, 26, 49631246523618756274n);

test/src/sequence.js

@@ -0,0 +1,11 @@
+import test from 'ava';
+
+import {list, take} from '@aureooms/js-itertools';
+
+import {sequence} from '../../src';
+
+test('sequence', (t) => {
+	const n = 7;
+	const expected = [1n, 1n, 2n, 5n, 15n, 52n, 203n];
+	t.deepEqual(list(take(sequence(), n)), expected);
+});