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%I #15 Sep 08 2022 08:44:51
%S 1,3,5,9,15,23,35,53,73,101,141,185,247,329,417,533,689,853,1061,1331,
%T 1613,1977,2429,2899,3485,4227,4989,5915,7049,8211,9643,11357,13111,
%U 15229,17799,20413,23497,27167,30899,35373,40609,45927,52171,59549,67015,75643
%N a(n) = a(n-1)+ a(round(2*(n-1)/3)) +a(round((n-1)/3)) starting a(1)=1.
%H G. C. Greubel, <a href="/A033498/b033498.txt">Table of n, a(n) for n = 1..1000</a>
%p A033498 := proc(n) option remember; if n <= 1 then 1 else A033498(n-1)+A033498(round(2*(n-1)/3))+A033498(round((n-1)/3)); fi; end;
%t a[n_]:= a[n]= If[n<2, 1, a[n-1] +a[Round[2*(n-1)/3]] +a[Round[(n-1)/3]]];
%t Table[a[n], {n, 50}] (* _G. C. Greubel_, Oct 14 2019 *)
%o (PARI) a(n) = if(n<2, 1, a(n-1)+a(round(2*(n-1)/3)) +a(round((n-1)/3)) );
%o vector(50, n, a(n) ) \\ _G. C. Greubel_, Oct 14 2019
%o (Magma) a:= func< n | n lt 2 select 1 else Self(n-1) + Self(Round(2*(n-1)/3)) + Self(Round((n-1)/3)) >;
%o [a(n): n in [1..50]]; // _G. C. Greubel_, Oct 14 2019
%o (Sage)
%o @CachedFunction
%o def a(n):
%o if (n<2): return 1
%o else: return a(n-1) +a(round(2*(n-1)/3)) +a(round((n-1)/3))
%o [a(n) for n in (1..50)] # _G. C. Greubel_, Oct 14 2019
%Y Cf. A033499, A033500.
%K nonn
%O 1,2
%A _N. J. A. Sloane_
%E Terms a(39) and onward added by _G. C. Greubel_, Oct 14 2019
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