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Module[{f},​​f[n_]:=f[n]=If[n<=2,n,f[n-1]+f[n-2]];​​LogPlot[f[n],{n,0,30}]]
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Module[{f},​​f[n_]:=f[n]=If[n<=2,n,f[n-1]+1];​​Plot[f[n],{n,0,30}]]
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Module[{f},​​f[n_]:=f[n]=If[n<=0,n,f[n-3/2]+1/3];​​Plot[f[n],{n,0,30},PlotRange->All]]
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Module[{f},​​f[n_]:=f[n]=If[n<=2,n,3+f[n-f[n-2]]];​​Plot[f[n],{n,0,100},PlotRange->All]]
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Module[{f},​​f[n_]:=f[n]=If[n<=4,n,2f[n-1f[n-2]]];​​Plot[f[n],{n,0,100},PlotRange->All]]
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TerminatedEvaluation[RecursionLimit]
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Module[{f},​​f[n_]:=f[n]=If[n<=1,n,n-f[f[n-2]]];​​Plot[f[n],{n,0,100},PlotRange->All]]
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Module[{f},​​f[n_]:=f[n]=If[n<=1,n,n-f[f[n-1]]];​​Plot[f[n],{n,0,20},PlotRange->All]]
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Module[{f},​​f[n_]:=f[n]=If[n<=1,n,n-f[f[n-4]]];​​Plot[f[n],{n,0,100},PlotRange->All]]
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designation
recursion
asymptotics
initial condition
Plus-like
Pabc
a+f[n-bf[n-c]]
~
n
finite
Times-like
Tabc
af[n-bf[n-c]]
~
α
n
(?)
infinite
Minus-like
Mab
n-f[f[n-a]-b]
~ αn
finite
f[n_/;n<1]=1;f[n_]:=3+f[n-f[n-2]]
f[n]->2f[n-1f[n-2]]
Lookbacks?
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ListStepPlot[RecursiveFunction[​​f[n]->n-f[f[n-1]],​​{}->{},​​{n<=3->3}​​][Range[200]]-Table[n/GoldenRatio,{n,200}],Center,AspectRatio->1/4,Frame->True]
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