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

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, 53, 62, 71, 83, 96, 111, 129, 149, 173, 200, 232, 268, 311, 360, 417, 483, 560, 648, 751, 869, 1007, 1166

Offset: 0

Author

Roger L. Bagula, Nov 29 2010

Keywords

• nonn
• less

Comments

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

Crossrefs

Cf. A174427.

Programs

Mathematica

a = (1 + 3^(1/4))/2; b = (1 - 3^(1/4))/2;
f[n_] := Floor[FullSimplify[(a^n - b^n)/(a - b)]]
Table[f[n], {n, 0, 50}]