A187362 Pell trisection: Pell(3*n+2), n >= 0.

2, 29, 408, 5741, 80782, 1136689, 15994428, 225058681, 3166815962, 44560482149, 627013566048, 8822750406821, 124145519261542, 1746860020068409, 24580185800219268, 345869461223138161, 4866752642924153522, 68480406462161287469, 963592443113182178088, 13558774610046711780701

Offset

0,1

Comments

For the general trisection of a sequence see a Wolfdieter Lang comment under A187357.

Links

Colin Barker, Table of n, a(n) for n = 0..850

Index entries for linear recurrences with constant coefficients, signature (14,1).

Formula

a(n) = Pell(3*n+2), n >= 0, with Pell(n):=A000129(n).

O.g.f.: (2+x)/(1-14*x-x^2).

a(n) = 14*a(n-1) + a(n-2), a(-1)=1, a(0)=2.

a(n) = (((7-5*sqrt(2))^n*(-3+2*sqrt(2)) + (3+2*sqrt(2))*(7+5*sqrt(2))^n)) / (2*sqrt(2)). - Colin Barker, Jan 25 2016

Mathematica

Table[Fibonacci[3n + 2, 2], {n, 0, 20}] (* Vladimir Reshetnikov, Sep 16 2016 *)

Prog

(PARI) Vec((2+x)/(1-14*x-x^2) + O(x^20)) \\ Colin Barker, Jan 25 2016

Crossrefs

Cf. A142588 (Pell(3n)), A187361 (Pell(3n+1)).

Sequence in context: A183722 A104535 A264175 * A176938 A006988 A282735

Adjacent sequences: A187359 A187360 A187361 * A187363 A187364 A187365

Keyword

nonn,easy

Author

Wolfdieter Lang, Mar 09 2011

Status

approved