A199493 a(n) = 2*8^n + 1.

3, 17, 129, 1025, 8193, 65537, 524289, 4194305, 33554433, 268435457, 2147483649, 17179869185, 137438953473, 1099511627777, 8796093022209, 70368744177665, 562949953421313, 4503599627370497, 36028797018963969, 288230376151711745, 2305843009213693953

Offset

0,1

Comments

An Engel expansion of 4 to the base 8 as defined in A181565, with the associated series expansion 4 = 8/3 + 8^2/(3*17) + 8^3/(3*17*129) + 8^4/(3*17*129*1025) + .... Cf. A087289 and A199552. - Peter Bala, Oct 30 2013

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (9,-8).

Formula

a(n) = 8*a(n-1) - 7.

a(n) = 9*a(n-1) - 8*a(n-2).

G.f.: (3-10*x)/((1-x)*(1-8*x)).

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

E.g.f.: exp(x)*(1 + 2*exp(7*x)).

a(n) = A013730(n) + 1. (End)

Mathematica

2*8^Range[0, 20] + 1 (* Wesley Ivan Hurt, Jul 23 2025 *)

Prog

(Magma) [2*8^n+1: n in [0..30]];

Crossrefs

Cf. A013730, A087289, A181565, A199552.

Sequence in context: A093460 A187613 A179300 * A245059 A321587 A385468

Adjacent sequences: A199490 A199491 A199492 * A199494 A199495 A199496

Keyword

nonn,easy

Author

Vincenzo Librandi, Nov 07 2011

Status

approved