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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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