Fibonacci Sequences

Many readers will be familiar with the famous sequence <m:math display='block'> <m:mrow> <m:mn>1</m:mn><m:mo>,</m:mo><m:mn>1</m:mn><m:mo>,</m:mo><m:mn>2</m:mn><m:mo>,</m:mo><m:mn>3</m:mn><m:mo>,</m:mo><m:mn>5</m:mn><m:mo>,</m:mo><m:mn>8</m:mn><m:mo>,</m:mo><m:mn>13</m:mn><m:mo>,</m:mo><m:mn>...</m:mn> </m:mrow> </m:math>]]</EquationSource><EquationSource Format="TEX"><![CDATA[$$1,1,2,3,5,8,13,...$$ in which each term after the second is obtained by adding the previous two terms. It was known at least as early as 1226 when Leonardo Fibonacci of Pisa propounded his problem concerning the proliferation of a hypothetical pair of rabbits: each pair of newborn rabbits is assumed to bear its first pair two months later and thereafter to bear one pair a month. (See N. N. Vorob’ev, Fibonacci Numbers, Popular Lectures in Mathematics, Vol. 2).