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A007455
Number of subsequences of [ 1,...,n ] in which each odd number has an even neighbor.
(Formerly M2480)
4
1, 1, 3, 5, 11, 17, 39, 61, 139, 217, 495, 773, 1763, 2753, 6279, 9805, 22363, 34921, 79647, 124373, 283667, 442961, 1010295, 1577629, 3598219, 5618809, 12815247, 20011685, 45642179, 71272673, 162557031, 253841389, 578955451, 904069513
OFFSET
0,3
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
R. K. Guy, William O. J. Moser, Numbers of subsequences without isolated odd members, Fibonacci Quarterly, 34, No. 2, 152-155 (1996).
FORMULA
a(n) = 3*a(n-2) + 2*a(n-4).
G.f. = (1 + x + 2 x^3)/(1 - 3 x^2 - 2 x^4). - Harvey P. Dale, Feb 18 2011, edited by M. F. Hasler, Jun 19 2019
MATHEMATICA
CoefficientList[Series[(-1-x-2 x^3)/(-1+3 x^2+2 x^4), {x, 0, 40}], x] (* Harvey P. Dale, Feb 18 2011 *)
LinearRecurrence[{0, 3, 0, 2}, {1, 1, 3, 5}, 40] (* Harvey P. Dale, Feb 10 2015 *)
PROG
(Haskell)
a007455_list = 1 : 1 : 3 : 5 : zipWith (+)
(map (* 2) a007455_list) (map (* 3) $ drop 2 a007455_list)
a007455 n = a007455_list !! n
-- Reinhard Zumkeller, Jul 16 2012
(PARI) A007455(n)=[n%2*2+3, 1]*([3, 1; 2, 0]^(n\2-1))[, 1] \\ M. F. Hasler, Jun 19 2019
CROSSREFS
KEYWORD
nonn,easy,nice
STATUS
approved