Editing Fibonacci sequence (section)

==Definition==
[[File:Fibonacci Spiral.svg|thumb|The Fibonacci spiral: an approximation of the [[golden spiral]] created by drawing [[circular arc]]s connecting the opposite corners of squares in the Fibonacci tiling (see preceding image)]]

The Fibonacci numbers may be defined by the [[recurrence relation]]{{Sfn | Lucas | 1891 | p=3}}
<math display=block>F_0=0,\quad F_1= 1,</math>
and
<math display=block>F_n=F_{n-1} + F_{n-2}</math>
for {{math|''n'' > 1}}.

Under some older definitions, the value <math>F_0 = 0</math> is omitted, so that the sequence starts with <math>F_1=F_2=1,</math> and the recurrence <math>F_n=F_{n-1} + F_{n-2}</math> is valid for {{math|''n'' > 2}}.{{Sfn | Beck | Geoghegan | 2010}}{{Sfn | Bóna | 2011 | p=180}} <!--Fibonacci started the sequence with index 0: {{math|<sub>0</sub>→1, <sub>1</sub>→2, <sub>2</sub>→3, ..., <sub>12</sub>→377}}.<ref>{{citation |last1=Leonardo da Pisa |title=File:Liber abbaci magliab f124r.jpg - Wikimedia Commons |date=1202 |url=https://commons.wikimedia.org/wiki/File:Liber_abbaci_magliab_f124r.jpg |language=en}}</ref>-->

The first 20 Fibonacci numbers {{math|''F<sub>n</sub>''}} are:
:{| class="wikitable" style="text-align:right"
! {{math|''F''<sub>0</sub>}}
! {{math|''F''<sub>1</sub>}}
! {{math|''F''<sub>2</sub>}}
! {{math|''F''<sub>3</sub>}}
! {{math|''F''<sub>4</sub>}}
! {{math|''F''<sub>5</sub>}}
! {{math|''F''<sub>6</sub>}}
! {{math|''F''<sub>7</sub>}}
! {{math|''F''<sub>8</sub>}}
! {{math|''F''<sub>9</sub>}}
! {{math|''F''<sub>10</sub>}}
! {{math|''F''<sub>11</sub>}}
! {{math|''F''<sub>12</sub>}}
! {{math|''F''<sub>13</sub>}}
! {{math|''F''<sub>14</sub>}}
! {{math|''F''<sub>15</sub>}}
! {{math|''F''<sub>16</sub>}}
! {{math|''F''<sub>17</sub>}}
! {{math|''F''<sub>18</sub>}}
! {{math|''F''<sub>19</sub>}}
|-
| 0
| 1
| 1
| 2
| 3
| 5
| 8
| 13
| 21
| 34
| 55
| 89
| 144
| 233
| 377
| 610
| 987
| 1597
| 2584
| 4181
|}