A380001 Fixed points of A378299.

0, 1, 13, 109, 877, 7021, 56173, 449389, 3595117, 28760941, 230087533, 1840700269, 14725602157, 117804817261, 942438538093, 7539508304749, 60316066437997, 482528531503981, 3860228252031853, 30881826016254829, 247054608130038637, 1976436865040309101, 15811494920322472813

Offset

0,3

Links

Paolo Xausa, Table of n, a(n) for n = 0..1000

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

Formula

a(0) = 0; a(1) = 1; a(n) = 8*a(n-1) + 5, for n > 1.

From Elmo R. Oliveira, Mar 12 2026: (Start)

G.f.: x*(4*x + 1)/((x - 1)*(8*x - 1)).

E.g.f.: (7 - 10*exp(x) + 3*exp(8*x))/14.

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

a(n) = (3*8^n - 10)/14 for n > 0. (End)

Example

For n >= 1, the binary representation of a(n) is 1 followed by (101 repeated n-1 times).
E.g., a(5) = 7021 = (1 101 101 101 101)_2.

Mathematica

Join[{0}, NestList[8*# + 5 &, 1, 25]]

Crossrefs

Cf. A378299.

Sequence in context: A243417 A367592 A163845 * A075143 A005769 A042941

Adjacent sequences: A379998 A379999 A380000 * A380002 A380003 A380004

Keyword

nonn,base,easy

Author

Paolo Xausa, Jan 10 2025

Status

approved