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%I #23 May 07 2021 09:19:50
%S 1,1,1,1,2,2,2,2,2,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,7,7,7,7,7,7,7,7,7,
%T 7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,11,11,11,11,11,11,11,11,11,11,11,11,11,
%U 11,11,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13
%N a(n) is the number of ways n can be reached starting from 0 and using only two operations: adding one or, once n > 1, squaring.
%F a(n) = a(n-1) + a(sqrt(n)) if n is a square or a(n-1) otherwise.
%t a[0]:=1; a[n_]:=If[IntegerQ[Sqrt[n]],a[n-1]+a[Sqrt[n]],a[n-1]]; Table[a[n],{n,0,80}] (* _Stefano Spezia_, May 06 2021 *)
%Y Cf. A097046.
%K nonn
%O 0,5
%A _James P. B. Hall_, Apr 09 2021