A028894 -id:A028894 - cp's OEIS frontend

A140529 a(n) = 6*4^n - 1.

5, 23, 95, 383, 1535, 6143, 24575, 98303, 393215, 1572863, 6291455, 25165823, 100663295, 402653183, 1610612735, 6442450943, 25769803775, 103079215103, 412316860415, 1649267441663, 6597069766655, 26388279066623, 105553116266495

Offset: 0

Paul Curtz, Jul 03 2008

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-4).

Cf. A028894.

[6*4^n-1: n in [0..30]]; // Vincenzo Librandi, Aug 08 2011

NestList[4#+3&,5,30] (* Harvey P. Dale, Jan 14 2022 *)

a(n) = 4*a(n-1) + 3, a(0)=5.
a(n) = A002023(n) - 1 = A000302(n+1) + A083420(n).
G.f.: ( 5-2*x ) / ( (4*x-1)*(x-1) ). - R. J. Mathar, Jul 08 2022

A066744 a(n) = either 4a(n-1)+1 or 4a(n-1)+3 depending on corresponding term of A005614, +3 for 0, +1 for 1.

Original entry on oeis.org

1, 7, 29, 117, 471, 1885, 7543, 30173, 120693, 482775, 1931101, 7724405, 30897623, 123590493, 494361975, 1977447901, 7909791605, 31639166423, 126556665693, 506226662775, 2024906651101, 8099626604405, 32398506417623

Offset: 1

John McNamara, Jan 16 2002

nonn

Ratio to terms of A028894 tends to 1.23459972586...

Related to A005614, A002450, A037576, A028894.

f[1]={0}; f[2]={1}; f[n_] := f[n]=Join[f[n-1], f[n-2]]; a[1]=1; a[n_] := a[n]=4a[n-1]+3-2f[9][[n]]; a/@Range[1, 30]

cp's OEIS Frontend

A140529 a(n) = 6*4^n - 1.

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