In the 1700s, his interest in economic forecasting led him to write a text entitled La Cochonnerie ou calcul estimatif pour connaître jusqu’où peut aller la production d’une truie pendant dix années de temps (Pig Farming, or an estimate of how many offspring a sow can produce over ten years). In it, he shows that after twelve generations, a single sow has enough descendants to feed the whole of Europe!
To allow for various losses—disease, accidents and pigs taken by wolves—Vauban assumes that each litter consists of six piglets: three females, which are counted in the calculation, and three males, which play no further part in it. In his model, a sow has her first litter in her second year, then two litters a year for four years, before becoming sterile in her seventh year. If T*n denotes the number of sows born in the n-*th year, we obtain the recurrence relation:
T*n = 3Tn*‒1 + 6T*n*‒2 + 6T*n*‒3 + 6T*n*‒4 + 6T*n*‒5 for n ≥ 2, with T*n = 0 for n* ≤ 0 and T1 = 1.
The resulting values, known as the Vauban numbers, are: 1, 3, 15, 69, 321, 1,491, 6,921, 32,139… They increase very rapidly!
