OFFSET
1,3
COMMENTS
This sequence is connected with the Collatz problem (see the sequences A045883 and A001045). - Michel Lagneau, Jan 13 2012
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
T. Etzion, On the stopping redundancy of Reed-Muller codes, IEEE Trans. Information Theory 52 (11) (2006) 4867-4879; arXiv:cs.IT/0511056.
Index entries for linear recurrences with constant coefficients, signature (3,0,-4).
FORMULA
a(n+1) - 2*a(n) = A001045(n+2), Jacobsthal numbers. - Paul Curtz, Jul 05 2008
3*a(n) - a(n+1) = -1, -2, 4*a(n). - Paul Curtz, Jul 05 2008
From R. J. Mathar, Nov 11 2008: (Start)
G.f.: x^2*(1+2*x)/((1+x)*(1-2*x)^2).
a(n) + a(n+1) = A014480(n-1). (End)
a(n) = 4*a(n-1) - 4*a(n-2) + (-1)^(n+1), n>2. - Gary Detlefs, Dec 19 2010
a(n) = 3*a(n-1) - 4*a(n-3), n>3. - Gary Detlefs, Dec 19 2010
a(n) = n*2^n - A045883(n). - Michel Lagneau, Jan 13 2012
Starting with "1" = triangle A059260 * A016813 as a vector, where A016813 = (4n + 1): [ 1, 5, 9, 13, ...]. - Gary W. Adamson, Mar 06 2012
MATHEMATICA
Join[{0}, Numerator[CoefficientList[Series[(x+1)/((x-1)*(x^2+x-2)), {x, 0, 40}], x]]] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2012 *)
LinearRecurrence[{3, 0, -4}, {0, 1, 5}, 40] (* Harvey P. Dale, Jun 16 2022 *)
PROG
(PARI) a(n)=((6*n-7)<<(n-1)-(-1)^n)/9 \\ Charles R Greathouse IV, Jan 13 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jan 25 2006
STATUS
approved