A187560 a(n) = 4^(n+1)-2^n-1.

2, 13, 59, 247, 1007, 4063, 16319, 65407, 261887, 1048063, 4193279, 16775167, 67104767, 268427263, 1073725439, 4294934527, 17179803647, 68719345663, 274877644799, 1099511103487, 4398045462527, 17592183947263, 70368739983359, 281474968322047, 1125899890065407

Offset: 0

Author

Brad Clardy, Mar 25 2011

Keywords

• nonn
• easy

Comments

For n>0, binary numbers of the form (n+1)0 n, where n is the index value and the number of 1's. This can be formed by appending a leading 1 to the terms of A129868. It is also A156589 written in bit-reverse order.

Examples

			Binary values of the first 7 terms are 10, 1101, 111011, 11110111, 1111101111, 111111011111, 11111110111111.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (7,-14,8).

Crossrefs

Cf. A171499.

Programs

Mathematica

Table[4^(n+1)-2^n-1,{n,0,30}] (* or *) LinearRecurrence[{7,-14,8},{2,13,59},30] (* Harvey P. Dale, Feb 25 2013 *)

PARI

a(n)=4^(n+1)-2^n-1 \\ Charles R Greathouse IV, Nov 01 2015

Formula

a(n) = 4^(n+1)-2^n-1 = A171499(n)-1.

G.f.: ( -2+x+4*x^2 ) / ( (x-1)*(2*x-1)*(4*x-1) ). - R. J. Mathar, Apr 09 2011

a(0)=2, a(1)=13, a(2)=59, a(n)=7*a(n-1)-14*a(n-2)+8*a(n-3). - Harvey P. Dale, Feb 25 2013

E.g.f.: exp(x)*(4*exp(3*x) - exp(x) - 1). - Stefano Spezia, Apr 11 2025

Extensions

Terms a(21) and beyond from Andrew Howroyd, Feb 25 2018