OFFSET
0,2
COMMENTS
A055099(n) = a(2*n+1) - a(2*n) = a(2*(n+1)) - a(2*n+1). - Reinhard Zumkeller, Oct 25 2015
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
T. D. Noe, Table of n, a(n) for n = 0..400
R. K. Guy and W. O. J. Moser, Numbers of subsequences without isolated odd members, Fibonacci Quarterly 34:2 (1996), pp. 152-155.
Index entries for linear recurrences with constant coefficients, signature (0, 3, 0, 2).
FORMULA
a(n) = 3*a(n-2) + 2*a(n-4).
G.f.: (x^3+2*x+1)/(-2*x^4-3*x^2+1). - Harvey P. Dale, Feb 29 2012
EXAMPLE
For n=2, there are the following three subsequences of [1,2] with the desired property: empty, [1], [1,2].
For n=3, there are the following seven subsequences of [1,2,3] with the desired property: empty, [1], [3], [1,2], [2,3], [1,3], [1,2,3].
MATHEMATICA
LinearRecurrence[{0, 3, 0, 2}, {1, 2, 3, 7}, 40] (* Harvey P. Dale, Feb 29 2012 *)
PROG
(Haskell)
a007481 n = a007481_list !! n
a007481_list = 1 : 2 : 3 : 7 : zipWith (+)
(map (* 3) $ drop 2 a007481_list) (map (* 2) a007481_list)
-- Reinhard Zumkeller, Oct 25 2015
(PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; 2, 0, 3, 0]^n*[1; 2; 3; 7])[1, 1] \\ Charles R Greathouse IV, Mar 02 2016
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
EXTENSIONS
More terms from James Sellers, Dec 24 1999
STATUS
approved