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A104863 a(n) = floor(sqrt(a(n-1)^2 + a(n-2)^2)), a(1)=10, a(2)=30.

%I A104863 #21 Sep 08 2022 08:45:17
%S A104863 10,30,31,43,53,68,86,109,138,175,222,282,358,455,578,735,935,1189,
%T A104863 1512,1923,2446,3111,3957,5033,6402,8143,10358,13175,16759,21317,
%U A104863 27116,34491,43873,55807,70987,90297,114859,146103,185845,236398,300703,382500,486547,618897
%N A104863 a(n) = floor(sqrt(a(n-1)^2 + a(n-2)^2)), a(1)=10, a(2)=30.
%H A104863 Harvey P. Dale, <a href="/A104863/b104863.txt">Table of n, a(n) for n = 1..1000</a>
%F A104863 For n>=17, a(n) = a(n-2) + a(n-4) + 1 (conjectured). If true then for m>5, a(2*m+1) = 4*F(m) + 25*F(m+1) + 1 and a(2*m+2) = 8*F(m) + 30*F(m+1) + 1 with F(n) = A000045(n). - _Ralf Stephan_, Nov 15 2010
%t A104863 nxt[{a_,b_}]:={b,Floor[Sqrt[a^2+b^2]]}; Transpose[NestList[nxt,{10,30},60]][[1]] (* _Harvey P. Dale_, Jun 18 2013 *)
%o A104863 (Magma)
%o A104863 A104863:= func< n| n lt 3 select 10*(2*n-1) else Floor(Sqrt(Self(n-1)^2 +Self(n-2)^2)) >;
%o A104863 [A104863(n): n in [1..60]]; // _G. C. Greubel_, Jun 27 2021
%o A104863 (Sage)
%o A104863 @CachedFunction
%o A104863 def a(n): return 10*(2*n-1) if (n<3) else floor(sqrt(a(n-1)^2 + a(n-2)^2))
%o A104863 [a(n) for n in (1..60)] # _G. C. Greubel_, Jun 27 2021
%Y A104863 Cf. A104803, A104804, A104805, A104806, A104864.
%K A104863 nonn
%O A104863 1,1
%A A104863 _Zak Seidov_, Mar 28 2005