A104863 a(n) = floor(sqrt(a(n-1)^2 + a(n-2)^2)), a(1)=10, a(2)=30.
10, 30, 31, 43, 53, 68, 86, 109, 138, 175, 222, 282, 358, 455, 578, 735, 935, 1189, 1512, 1923, 2446, 3111, 3957, 5033, 6402, 8143, 10358, 13175, 16759, 21317, 27116, 34491, 43873, 55807, 70987, 90297, 114859, 146103, 185845, 236398, 300703, 382500, 486547, 618897
Offset: 1
Keywords
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..1000
Programs
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Magma
A104863:= func< n| n lt 3 select 10*(2*n-1) else Floor(Sqrt(Self(n-1)^2 +Self(n-2)^2)) >; [A104863(n): n in [1..60]]; // G. C. Greubel, Jun 27 2021
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Mathematica
nxt[{a_,b_}]:={b,Floor[Sqrt[a^2+b^2]]}; Transpose[NestList[nxt,{10,30},60]][[1]] (* Harvey P. Dale, Jun 18 2013 *) -
Sage
@CachedFunction def a(n): return 10*(2*n-1) if (n<3) else floor(sqrt(a(n-1)^2 + a(n-2)^2)) [a(n) for n in (1..60)] # G. C. Greubel, Jun 27 2021
Formula
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