manhattan.py

#!/bin/python3

# manhattan.py
# Solves "paths of Manhattan (2d)" problem
#
# Copyright(C) 2020 rw-r-r-0644
# This file is under GNU GPLv2
import math, sys

def tartaglia(n, k):
	return math.factorial(n) // (math.factorial(k) * math.factorial(n - k))

def manhattan(i, j):
	return tartaglia(i + j, min(i, j))

i = int(sys.argv[1])
j = int(sys.argv[2])
print(manhattan(i, j))

manhattan.rkt

; manhattan.rkt
; Solves "paths of Manhattan (2d)" problem
;
; Copyright(C) 2020 rw-r-r-0644
; This file is under GNU GPLv2

(define factorial
  (lambda (n)
    (if (= n 0) 1
        (* n (factorial (- n 1))))
    ))

(define tartaglia
  (lambda (n k)
    (quotient (factorial n) (* (factorial k) (factorial (- n k))))
    ))

(define manhattan-2d
  (lambda (i j)
    (tartaglia (+ i j) (min i j))
    ))