A077631 Sum of terms in periodic part of continued fraction expansion of square root of -1 + 3^n.

2, 5, 10, 17, 56, 53, 160, 161, 346, 485, 1850, 1457, 3764, 4373, 13468, 13121, 43572, 39365, 192642, 118097, 226348, 354293, 2646006, 1062881, 1871694, 3188645, 5646564, 9565937, 36393508, 28697813, 143274092, 86093441, 195407590, 258280325, 542628818, 774840977

Offset: 1

Author

Labos Elemer, Nov 13 2002

Keywords

• nonn

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..52

Crossrefs

Cf. A077624-A077635.

Programs

Mathematica

Table[Apply[Plus, Last[ContinuedFraction[Sqrt[ -1+3^u]]]], {u, 1, 25}]

Formula

From Benoit Cloitre, Nov 28 2002: (Start)

a(2n) = 2*3^n-1.

Conjecture: if n>1 sqrt(3^(2n+1)) < a(2n+1) < sqrt((2n+1)*3^(2n+1)). (End)

Extensions

a(26)-a(36) from Chai Wah Wu, Sep 18 2021