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%I #30 Sep 27 2023 10:09:23
%S 1,3,5,7,9,9,15,15,17,19,19,19,29,29,29,29,31,31,41,41,41,41,41,41,55,
%T 55,55,57,57,57,57,57,59,59,59,59,85,85,85,85,85,85,85,85,85,85,85,85,
%U 103,103,103,103,103,103,117,117
%N a(n) = a(floor(n/2)) + a(floor(n/3)) + a(floor(n/6)).
%H T. D. Noe, <a href="/A007731/b007731.txt">Table of n, a(n) for n = 0..10000</a>
%H P. Erdős, A. Hildebrand, A. Odlyzko, P. Pudaite and B. Reznick, <a href="http://www.dtc.umn.edu/~odlyzko/doc/enumeration.html">The asymptotic behavior of a family of sequences</a>, Pacific J. Math., 126 (1987), pp. 227-241.
%F From given link, a(n) is asymptotic to c*n where c = 12/log(432) = 1.97744865... - _Benoit Cloitre_, Dec 18 2002
%p A007731 := proc(n) option remember; if n=0 then RETURN(1) else RETURN( A007731(trunc(n/2))+A007731(trunc(n/3))+A007731(trunc(n/6))); fi; end;
%p # second Maple program:
%p a:= proc(n) option remember; `if`(n=0, 1,
%p add(a(floor(n/i)), i=[2, 3, 6]))
%p end:
%p seq(a(n), n=0..100); # _Alois P. Heinz_, Sep 27 2023
%t a[n_] := a[n] = a[Floor[n/2]] + a[Floor[n/3]] + a[Floor[n/6]] ; a[0] = 1; Table[a[n], {n, 0, 60}] (* _Jean-François Alcover_, Mar 06 2014 *)
%o (Haskell)
%o a007731 n = a007731_list !! n
%o a007731_list = 1 : (zipWith3 (\u v w -> u + v + w)
%o (map (a007731 . (`div` 2)) [1..])
%o (map (a007731 . (`div` 3)) [1..])
%o (map (a007731 . (`div` 6)) [1..]))
%o -- _Reinhard Zumkeller_, Jan 11 2014
%o (PARI) a(n)=if(n<5, 2*n+1, a(n\2) + a(n\3) + a(n\6)) \\ _Charles R Greathouse IV_, Feb 08 2017
%Y Cf. A083662, A088468, A165704, A165706, A061984.
%K nonn,easy,nice
%O 0,2
%A _N. J. A. Sloane_
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