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A004766 Numbers whose binary expansion ends 01. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

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

a(n) = 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]

a(n) = 2*a(n-1)-a(n-2). G.f.: -x*(x-5) / (x-1)^2. - Colin Barker, Jun 24 2013

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 *)

PROG

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

CROSSREFS

Essentially same as A016813.

Sequence in context: A141135 A194395 A162502 * A016813 A198395 A190951

Adjacent sequences:  A004763 A004764 A004765 * A004767 A004768 A004769

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified March 28 19:06 EDT 2017. Contains 284246 sequences.