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
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved