A145641 Numbers whose binary representation is the concatenation of n 1's, n 0's and n 1's.

5, 51, 455, 3855, 31775, 258111, 2080895, 16711935, 133956095, 1072694271, 8585742335, 68702703615, 549688713215, 4397778092031, 35183298379775, 281470681808895, 2251782633947135, 18014329790267391, 144114913198473215, 1152920405096267775, 9223367638810361855

Offset: 1

Author

Omar E. Pol, Oct 14 2008

Keywords

• easy
• nonn
• base

Comments

Numbers whose binary representation are the members of A138721.

Links

• Paolo Xausa, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (15,-70,120,-64).

Crossrefs

Cf. A138721.

Programs

Maple

a:= n-> 8^n-4^n+2^n-1:
seq(a(n), n=1..30); # Alois P. Heinz, Nov 04 2012

Mathematica

Table[8^n - 4^n + 2^n - 1, {n, 25}] (* Paolo Xausa, Aug 08 2024 *)

Formula

G.f.: x*(40*x^2-24*x+5)/((x-1)*(2*x-1)*(4*x-1)*(8*x-1)). - Colin Barker, Nov 04 2012

a(n) = (2^n-1)*(2^(2*n)+1) = 8^n - 4^n + 2^n - 1. - Alois P. Heinz, Nov 04 2012

Extensions

More terms from Colin Barker, Nov 04 2012