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a(n) = floor( e^((n/2)*arccosh(1+sqrt(2))) ).
1

%I #9 Sep 08 2022 08:45:13

%S 1,2,4,9,21,45,98,210,452,971,2085,4478,9618,20654,44355,95252,204549,

%T 439262,943298,2025695,4350099,9341661,20060837,43079834,92512195,

%U 198666181,426627554,916165344,1967427861,4224971416,9072954499

%N a(n) = floor( e^((n/2)*arccosh(1+sqrt(2))) ).

%H G. C. Greubel, <a href="/A093698/b093698.txt">Table of n, a(n) for n = 0..1000</a>

%t Table[ Floor[E^(n/2*ArcCosh[1 + Sqrt[2]])], {n, 0, 30}]

%o (PARI) for(n=0,30, print1(floor(exp((n/2)*acosh(1+sqrt(2)))), ", ")) \\ _G. C. Greubel_, Oct 01 2018

%o (Magma) [Floor(Exp((n/2)*Argcosh(1+Sqrt(2)))): n in [0..30]]; // _G. C. Greubel_, Oct 01 2018

%Y Cf. A093568.

%K easy,nonn

%O 0,2

%A _Robert G. Wilson v_, Apr 09 2004