A004766 Numbers whose binary expansion ends 01.

5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, 65, 69, 73, 77, 81, 85, 89, 93, 97, 101, 105, 109, 113, 117, 121, 125, 129, 133, 137, 141, 145, 149, 153, 157, 161, 165, 169, 173, 177, 181, 185, 189, 193, 197, 201, 205, 209, 213, 217, 221, 225

Offset

1,1

Comments

These are the numbers for which zeta(2*x+1) needs just 3 terms to be evaluated. - Jorge Coveiro, Dec 16 2004

The binary representation of a(n) has exactly the same number of 0's and 1's as the binary representation of a(n+1). - Gil Broussard, Dec 18 2008

Number of monomials in n-th power of x^4+x^3+x^2+x+1. - Artur Jasinski, Oct 06 2008

Links

Table of n, a(n) for n=1..56.

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

a(n) = 8*n-a(n-1)-2 (with a(1)=5). - Vincenzo Librandi, Nov 18 2010

From Colin Barker, Jun 24 2013: (Start)

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

G.f.: -x*(x-5) / (x-1)^2. (End)

E.g.f.: exp(x)*(1 + 4*x) - 1. - Stefano Spezia, Feb 02 2023

Maple

seq( 4*x+1, x=1..100 );

Mathematica

a = {}; k = x^4 + x^3 + x^2 + x + 1; m = k; Do[AppendTo[a, Length[m]]; m = Expand[m*k], {n, 1, 100}]; a (* Artur Jasinski, Oct 06 2008 *)
Select[Range[2, 250], Take[IntegerDigits[#, 2], -2]=={0, 1}&] (* or *) LinearRecurrence[{2, -1}, {5, 9}, 70] (* Harvey P. Dale, Aug 07 2023 *)

Prog

(PARI) a(n)=4*n+1 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Essentially same as A016813.

Sequence in context: A363379 A194395 A162502 * A016813 A314668 A314669

Adjacent sequences: A004763 A004764 A004765 * A004767 A004768 A004769

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved