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.

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, 31, 36, 40, 46, 52, 60, 68, 77, 88, 100, 113, 129, 146, 166, 189, 214, 244, 277, 315, 357, 406, 461

Offset

0,9

Comments

A sequence designed to have limiting ratio:1.1360098247570344821

Links

Table of n, a(n) for n=0..50.

Mathematica

Clear[a, b, a0, f]
a0 = (1 + Sqrt[5])/2;
a = (1 + Sqrt[a0])/2; b = (1 - Sqrt[a0])/2;
f[n_] := Floor[FullSimplify[(a^n - b^n)/(a - b)]]
Table[f[n], {n, 0, 50}]

Crossrefs

Cf. A174575, A174427.

Sequence in context: A029159 A029099 A029245 * A288122 A060970 A035429

Adjacent sequences: A174573 A174574 A174575 * A174577 A174578 A174579

Keyword

nonn

Author

Roger L. Bagula, Nov 29 2010

Status

approved