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+;;; series.el --- Hosting common series of numbers -*- lexical-binding: t -*-
+;; Author: William Carroll <wpcarro@gmail.com>
+
+;;; Commentary:
+;; Encoding number series as I learn about them.
+;;
+;; These are the following series I'm interested in supporting:
+;; - Fibonacci
+;; - Catalan numbers
+;; - Figurate number series
+;;   - Triangular
+;;   - Square
+;;   - Pentagonal
+;;   - Hexagonal
+;;   - Lazy-caterer
+;; - Magic square
+;; - Look-and-say
+
+;;; Code:
+
+(require 'number)
+
+(defun series/range (beg end)
+  "Create a list of numbers from `BEG' to `END'.
+This is an inclusive number range."
+  (if (< end beg)
+      (list/reverse
+       (number-sequence end beg))
+    (number-sequence beg end)))
+
+(defun series/fibonacci-number (i)
+  "Return the number in the fibonacci series at `I'."
+  (cond
+   ((= 0 i) 0)
+   ((= 1 i) 1)
+   (t (+ (series/fibonacci-number (- i 1))
+         (series/fibonacci-number (- i 2))))))
+
+(defun series/fibonacci (n)
+  "Return the first `N' numbers of the fibonaccci series starting at zero."
+  (if (= 0 n)
+      '()
+    (list/reverse
+     (list/cons (series/fibonacci-number (number/dec n))
+                (list/reverse
+                 (series/fibonacci (number/dec n)))))))
+
+;; TODO: Consider memoization.
+(defun series/triangular-number (i)
+  "Return the number in the triangular series at `I'."
+  (if (= 0 i)
+      0
+    (+ i (series/triangular-number (number/dec i)))))
+
+;; TODO: Improve performance.
+;; TODO: Consider creating a stream protocol with `stream/next' and implement
+;; this using that.
+(defun series/triangular (n)
+  "Return the first `N' numbers of a triangular series starting at 0."
+  (if (= 0 n)
+      '()
+    (list/reverse
+     (list/cons (series/triangular-number (number/dec n))
+                (list/reverse
+                 (series/triangular (number/dec n)))))))
+
+(defun series/catalan-number (i)
+  "Return the catalan number in the series at `I'."
+  (if (= 0 i)
+      1
+    (/ (number/factorial (* 2 i))
+       (* (number/factorial (number/inc i))
+          (number/factorial i)))))
+
+(defun series/catalan (n)
+  "Return the first `N' numbers in a catalan series."
+  (->> (series/range 0 (number/dec n))
+       (list/map #'series/catalan-number)))
+
+(provide 'series)
+;;; series.el ends here