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A174575 a(n) = floor( (alpha^n-beta^n)/(alpha-beta) ), where alpha=(1 + 3^(1/4))/2 and beta = (1 - 3^(1/4))/2. 1

%I

%S 0,1,1,1,1,1,1,2,2,2,3,3,4,5,5,6,7,9,10,12,14,16,19,22,25,29,34,39,46,

%T 53,62,71,83,96,111,129,149,173,200,232,268,311,360,417,483,560,648,

%U 751,869,1007,1166

%N a(n) = floor( (alpha^n-beta^n)/(alpha-beta) ), where alpha=(1 + 3^(1/4))/2 and beta = (1 - 3^(1/4))/2.

%C The sequence is designed to have alpha as the limiting ratio of a(n+1)/a(n): 1.1580370064762462304...

%t a = (1 + 3^(1/4))/2; b = (1 - 3^(1/4))/2;

%t f[n_] := Floor[FullSimplify[(a^n - b^n)/(a - b)]]

%t Table[f[n], {n, 0, 50}]

%Y Cf. A174427.

%K nonn,less

%O 0,8

%A _Roger L. Bagula_, Nov 29 2010

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Last modified April 14 12:11 EDT 2021. Contains 342949 sequences. (Running on oeis4.)