A187361 Pell trisection: Pell(3*n+1), n >= 0.

1, 12, 169, 2378, 33461, 470832, 6625109, 93222358, 1311738121, 18457556052, 259717522849, 3654502875938, 51422757785981, 723573111879672, 10181446324101389, 143263821649299118, 2015874949414289041, 28365513113449345692, 399133058537705128729, 5616228332641321147898

Offset: 0

Author

Wolfdieter Lang, Mar 09 2011

Keywords

• nonn
• easy

Comments

For the general computation of the o.g.f.s for the trisection of a sequence, given by its real o.g.f., 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).

Crossrefs

Cf. A142588 (Pell(3*n)), A187362 (Pell(3*n+2)).

Programs

Mathematica

Table[Fibonacci[3n + 1, 2], {n, 0, 20}] (* Vladimir Reshetnikov, Sep 16 2016 *)
LinearRecurrence[{14,1},{1,12},20] (* Harvey P. Dale, Jul 06 2023 *)

PARI

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

Formula

a(n) = Pell(3*n+1), n >= 0, with Pell(n):=A000129(n).

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

a(n) = 14*a(n-1) + a(n-2), a(0)= 1, a(1)=12.

a(n) = (((7-5*sqrt(2))^n*(-1+sqrt(2))+(1+sqrt(2))*(7+5*sqrt(2))^n))/(2*sqrt(2)). - Colin Barker, Jan 25 2016