A198852 a(n) = 4*8^n - 1.

3, 31, 255, 2047, 16383, 131071, 1048575, 8388607, 67108863, 536870911, 4294967295, 34359738367, 274877906943, 2199023255551, 17592186044415, 140737488355327, 1125899906842623, 9007199254740991, 72057594037927935, 576460752303423487, 4611686018427387903

Offset: 0

Author

Vincenzo Librandi, Oct 31 2011

Keywords

• nonn
• easy

Comments

In base 8, the numbers of this sequence are written 37, 377, 3777, 37777, ... and satisfy the A052148 condition. - Michel Marcus, Aug 23 2013

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (9,-8).

Crossrefs

Cf. A013731, A052148.

Programs

Magma

[4*8^n-1: n in [0..30]];

Formula

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

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

G.f.: ( 3+4*x ) / ( (8*x-1)*(x-1) ). - R. J. Mathar, Oct 31 2011

a(n) = A013731(n) - 1. - Michel Marcus, Aug 23 2013

E.g.f.: exp(x)*(4*exp(7*x) - 1). - Stefano Spezia, May 29 2024