A199561 a(n) = 3*9^n + 1.

4, 28, 244, 2188, 19684, 177148, 1594324, 14348908, 129140164, 1162261468, 10460353204, 94143178828, 847288609444, 7625597484988, 68630377364884, 617673396283948, 5559060566555524, 50031545098999708, 450283905890997364, 4052555153018976268, 36472996377170786404

Offset: 0

Author

Vincenzo Librandi, Nov 08 2011

Keywords

• nonn
• easy

Comments

An Engel expansion of 3 to the base 9 as defined in A181565, with the associated series expansion 3 = 9/4 + 9^2/(4*28) + 9^3/(4*28*244) + 9^4/(4*28*244*2188) + .... Cf. A087289 and A207262. - Peter Bala, Oct 29 2013

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (10,-9).

Crossrefs

Cf. A066443, A087289, A181565, A199560, A207262.

Programs

Magma

[3*9^n+1: n in [0..30]];

Mathematica

3*9^Range[0,20]+1 (* or *) LinearRecurrence[{10,-9},{4,28},20] (* Harvey P. Dale, Jul 30 2019 *)

Formula

a(n) = 4*A066443(n).

a(n) = 9*a(n-1) - 8.

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

G.f.: 4*(1-3*x)/((1-x)*(1-9*x)).

From Elmo R. Oliveira, Sep 13 2024: (Start)

E.g.f.: exp(x)*(3*exp(8*x) + 1).

a(n) = 2*A199560(n). (End)