; Author: Yoonsuck Choe <choe(a)tamu.edu>
; 
; Given a pair of numbers, generate a sequence of pairs
; where the sum of the numbers in the pairs monotonically
; increases
;
; The pair should begin from '(0 1).
(defun gen-next (pair)
   (let* ((i (1+ (first pair)))
          (j (1+ (second pair)))
          (sum (+ i j)))
      (if (= i (1- sum))
         (list 0 (1- sum))
         (list i (- j 2)))))


; Test routines

(setq pair '(0 1))
(setq pair (gen-next pair))
(setq pair (gen-next pair))
(setq pair (gen-next pair))

; see how the pair evolves (the sum will monotonically increase)


; Test routines

; 1. Set up your array 
(setq test-array '(1 2 2 2 3 3 4 5 5 5 7 7 9 9 10))

(setq pair '(0 1))

; 2. Calculate the sum of the given pairs in list test-array.

(+ (nth (+ (first pair) 1) test-array) (nth  (+ (second pair) 1) test-array) )

; 3. Generate the next pair, and repeat

(setq pair (gen-next pair))
(+ (nth (+ (first pair) 1) test-array) (nth  (+ (second pair) 1) test-array) )