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A174576 a(n) = Floor[(alpha^n-beta^n)(alpha-beta)], with alpha = (1 + Sqrt(a0))/2; beta = (1 - Sqrt(a0))/2; a0=(1 + Sqrt(5))/2. 1

%I

%S 0,1,1,1,1,1,1,1,2,2,2,3,3,4,4,5,6,6,7,8,10,11,12,14,16,19,21,24,27,

%T 31,36,40,46,52,60,68,77,88,100,113,129,146,166,189,214,244,277,315,

%U 357,406,461

%N a(n) = Floor[(alpha^n-beta^n)(alpha-beta)], with alpha = (1 + Sqrt(a0))/2; beta = (1 - Sqrt(a0))/2; a0=(1 + Sqrt(5))/2.

%C A sequence designed to have limiting ratio:1.1360098247570344821

%t Clear[a, b, a0, f]

%t a0 = (1 + Sqrt[5])/2;

%t a = (1 + Sqrt[a0])/2; b = (1 - Sqrt[a0])/2;

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

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

%Y Cf. A174575, A174427.

%K nonn

%O 0,9

%A _Roger L. Bagula_, Nov 29 2010

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Last modified September 25 15:49 EDT 2020. Contains 337344 sequences. (Running on oeis4.)