A077630 Sum of terms in periodic part of continued fraction expansion of square root of 1+3^n.

0, 6, 18, 18, 86, 54, 344, 162, 650, 486, 3246, 1458, 11542, 4374, 19196, 13122, 83672, 39366, 434242, 118098, 248278, 354294, 5669112, 1062882, 10522426, 3188646, 5969216, 9565938, 46110338, 28697814, 271512140, 86093442, 149401156, 258280326, 583061114, 774840978

Offset: 1

Author

Labos Elemer, Nov 13 2002

Keywords

• nonn

Comments

a(1) = 0 since 3^1+1=4 is a square and sqrt(4) = 2 has no periodic part in its continued fraction expansion. - Chai Wah Wu, Sep 17 2021

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..48

Crossrefs

Cf. A077624-A077635.

Programs

Mathematica

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

Extensions

a(1) corrected and a(26)-a(36) added by Chai Wah Wu, Sep 17 2021