A137483 a(n+1) = 9*a(n) - 6, a(0) = 2.

2, 12, 102, 912, 8202, 73812, 664302, 5978712, 53808402, 484275612, 4358480502, 39226324512, 353036920602, 3177332285412, 28595990568702, 257363915118312, 2316275236064802, 20846477124583212, 187618294121248902, 1688564647091240112, 15197081823821161002

Offset

0,1

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (10,-9).

Formula

From Colin Barker, Feb 05 2016: (Start)

a(n) = (3 + 5*9^n)/4.

a(n) = 10*a(n-1) - 9*a(n-2) for n>1.

G.f.: 2*(1-4*x)/((1-x)*(1-9*x)). (End)

From Elmo R. Oliveira, Sep 19 2025: (Start)

E.g.f.: exp(x)*(3 + 5*exp(8*x))/4.

a(n) = A135522(2*n). (End)

Mathematica

RecurrenceTable[{a[1] == 2, a[n] == 9 a[n-1] - 6}, a, {n, 30}] (* Vincenzo Librandi, Feb 06 2016 *)

Prog

(PARI) a(n) = (3+5*9^n)/4 \\ Colin Barker, Feb 05 2016
(PARI) Vec(2*(1-4*x)/((1-x)*(1-9*x)) + O(x^25)) \\ Colin Barker, Feb 05 2016
(Magma) [n le 1 select 2 else 9*Self(n-1)-6: n in [1..30]]; // Vincenzo Librandi, Feb 06 2016

Crossrefs

First bisection of A135522.

Sequence in context: A202013 A151505 A096347 * A113557 A245266 A123897

Adjacent sequences: A137480 A137481 A137482 * A137484 A137485 A137486

Keyword

nonn,easy

Author

Paul Curtz, Apr 22 2008

Status

approved