n f(n-1)+f(n-2) 0 3 1 4 2 7 3 11 4 18 5 29 6 47 7 76 8 123 9 199 10 322 11 521 12 843 13 1364 14 2207 15 3571 16 5778 17 9349 18 15127 19 24476 20 39603 21 64079 22 103682 23 167761 24 271443 25 439204

Let's now look at the ratios again for the different pairs of terms. This is really interesting because the common ratios turn out to be exactly the same as they were for the Fibonacci sequence. No matter what two numbers we choose for f(0) and f(1), the common ratios will remain the same.

 n f(n-1)+f(n-2) Each pair Every other Every third Every fourth Every fifth 0 3 1.33333333333333 2.33333333333333 3.66666666666667 6 9.66666666666667 1 4 1.75 2.75 4.5 7.25 11.75 2 7 1.57142857142857 2.57142857142857 4.14285714285714 6.71428571428571 10.8571428571429 3 11 1.63636363636364 2.63636363636364 4.27272727272727 6.90909090909091 11.1818181818182 4 18 1.61111111111111 2.61111111111111 4.22222222222222 6.83333333333333 11.0555555555556 5 29 1.62068965517241 2.62068965517241 4.24137931034483 6.86206896551724 11.1034482758621 6 47 1.61702127659574 2.61702127659574 4.23404255319149 6.85106382978723 11.0851063829787 7 76 1.61842105263158 2.61842105263158 4.23684210526316 6.85526315789474 11.0921052631579 8 123 1.61788617886179 2.61788617886179 4.23577235772358 6.85365853658537 11.0894308943089 9 199 1.61809045226131 2.61809045226131 4.23618090452261 6.85427135678392 11.0904522613065 10 322 1.61801242236025 2.61801242236025 4.2360248447205 6.85403726708075 11.0900621118012 11 521 1.61804222648752 2.61804222648752 4.23608445297505 6.85412667946257 11.0902111324376 12 843 1.61803084223013 2.61803084223013 4.23606168446026 6.85409252669039 11.0901542111507 13 1364 1.61803519061584 2.61803519061584 4.23607038123167 6.85410557184751 11.0901759530792 14 2207 1.6180335296783 2.6180335296783 4.23606705935659 6.85410058903489 11.0901676483915 15 3571 1.61803416409969 2.61803416409969 4.23606832819938 6.85410249229908 11.0901708204985 16 5778 1.61803392177224 2.61803392177224 4.23606784354448 6.85410176531672 11.0901696088612 17 9349 1.61803401433308 2.61803401433308 4.23606802866617 6.85410204299925 11.0901700716654 18 15127 1.61803397897799 2.61803397897799 4.23606795795597 6.85410193693396 11.0901698948899 19 24476 1.61803399248243 2.61803399248243 4.23606798496486 6.8541019774473 11.0901699624122 20 39603 1.61803398732419 2.61803398732419 4.23606797464839 6.85410196197258 11.090169936621 21 64079 1.61803398929446 2.61803398929446 4.23606797858893 6.85410196788339 22 103682 1.61803398854189 2.61803398854189 4.23606797708378 23 167761 1.61803398882935 2.61803398882935 24 271443 1.61803398871955 25 439204