A174427 -id:A174427 - cp's OEIS frontend

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

Roger L. Bagula, Nov 29 2010

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

Cf. A174427.

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}]

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.

Original entry on oeis.org

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

Roger L. Bagula, Nov 29 2010

nonn

A sequence designed to have limiting ratio:1.1360098247570344821

Cf. A174575, A174427.

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}]

cp's OEIS Frontend

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

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