A156760 a(n) = 5*4^n - 1.

4, 19, 79, 319, 1279, 5119, 20479, 81919, 327679, 1310719, 5242879, 20971519, 83886079, 335544319, 1342177279, 5368709119, 21474836479, 85899345919, 343597383679, 1374389534719, 5497558138879, 21990232555519, 87960930222079, 351843720888319, 1407374883553279

Offset

0,1

Comments

Second column of the array A132207, or, if this array is flattened, a(n) = A132207(A007583(n)).

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (5,-4).

Formula

a(n) mod 9 = A070403(n+2).

a(n+1) = 10*A083420(n) + 9.

a(n) = 5*A000302(n) - 1.

a(n) = (A024036(n+1) + A140529(n))/2.

a(n) = 4*a(n-1) + 3, a(0)=4.

From R. J. Mathar, Feb 23 2009: (Start)

a(n) = A003947(n+1) - 1.

a(n) = 5*a(n-1) - 4*a(n-2).

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

a(n) = A198693(n) + 2^(2*n+1). - Bob Selcoe, Apr 20 2015

From Elmo R. Oliveira, Nov 16 2025: (Start)

E.g.f.: (5*exp(3*x) - 1)*exp(x).

a(n) = A199115(n) - 2. (End)

Example

Binary.......................................Decimal
100................................................4
10011.............................................19
1001111...........................................79
100111111........................................319
10011111111.....................................1279
1001111111111...................................5119
100111111111111................................20479
10011111111111111..............................81919
1001111111111111111...........................327679
100111111111111111111........................1310719
10011111111111111111111......................5242879
1001111111111111111111111...................20971519
100111111111111111111111111.................83886079
10011111111111111111111111111..............335544319
1001111111111111111111111111111...........1342177279
... - Philippe Deléham, Feb 23 2014

Mathematica

Table[5*4^n - 1, {n, 0, 18}] (* Michael De Vlieger, Apr 20 2015 *)

Prog

(Magma) [5*4^n-1: n in [0..30]]; // Vincenzo Librandi, Jul 02 2011

Crossrefs

Cf. A000302, A003947, A007583, A024036, A070403, A083420, A132207, A140529, A198693, A199115.

Sequence in context: A378499 A037681 A391693 * A320088 A122909 A215037

Adjacent sequences: A156757 A156758 A156759 * A156761 A156762 A156763

Keyword

nonn,easy

Author

Paul Curtz, Feb 15 2009

Extensions

Edited and extended by R. J. Mathar, Feb 23 2009

Status

approved