A177738 a(n) = floor( (x^n - x^(-n)) / (x - x^(-1)) ) where x = Pi-2.

0, 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 15, 17, 20, 23, 26, 30, 35, 40, 46, 52, 60, 69, 78, 90, 103, 117, 134, 153, 175, 199, 228, 260, 297, 339, 387, 442, 505, 576, 658, 751, 858, 979, 1118, 1277, 1457, 1664, 1900, 2169, 2476, 2826

Offset: 0

Author

Roger L. Bagula, May 12 2010

Keywords

• nonn

Comments

The ratio a(n+1)/a(n) approaches Pi-2 as n approaches infinity, and is lower than even Salem polynomial expansions based on A073011.

The idea is the emulation of quadratic beta integer domains using a transcendental number base with a ratio below A073011.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A073011, A029826, A000796.

Programs

Mathematica

Clear[a, n, b]; b = Pi - 2; a[n_] = (b^n - b^(-n))/(b - b^(-1));
Table[Floor[a[n]], {n, 0, 50}]

Extensions

Undefined terminology removed from the definition - The Assoc. Eds. of the OEIS, May 14 2010