;;; series.el --- Hosting common series of numbers -*- lexical-binding: t -*-

;; Author: William Carroll <wpcarro@gmail.com>
;; Version: 0.0.1
;; Package-Requires: ((emacs "24"))

;;; 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:

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;; Dependencies
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(require 'number)

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;; Library
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(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