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A104863
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a(n) = floor(sqrt(a(n-1)^2 + a(n-2)^2)), a(1)=10, a(2)=30.
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3
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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
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OFFSET
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1,1
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LINKS
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FORMULA
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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
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MATHEMATICA
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nxt[{a_, b_}]:={b, Floor[Sqrt[a^2+b^2]]}; Transpose[NestList[nxt, {10, 30}, 60]][[1]] (* Harvey P. Dale, Jun 18 2013 *)
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PROG
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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)) >;
(Sage)
@CachedFunction
def a(n): return 10*(2*n-1) if (n<3) else floor(sqrt(a(n-1)^2 + a(n-2)^2))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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