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A007455 Number of subsequences of [ 1,...,n ] in which each odd number has an even neighbor.

%I A007455 M2480 #33 Jan 05 2025 19:51:34
%S A007455 1,1,3,5,11,17,39,61,139,217,495,773,1763,2753,6279,9805,22363,34921,
%T A007455 79647,124373,283667,442961,1010295,1577629,3598219,5618809,12815247,
%U A007455 20011685,45642179,71272673,162557031,253841389,578955451,904069513
%N A007455 Number of subsequences of [ 1,...,n ] in which each odd number has an even neighbor.
%D A007455 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A007455 T. D. Noe, <a href="/A007455/b007455.txt">Table of n, a(n) for n=0..400</a>
%H A007455 R. K. Guy, William O. J. Moser, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/34-2/guy.pdf">Numbers of subsequences without isolated odd members</a>, Fibonacci Quarterly, 34, No. 2, 152-155 (1996).
%H A007455 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,2).
%F A007455 a(n) = 3*a(n-2) + 2*a(n-4).
%F A007455 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
%t A007455 CoefficientList[Series[(-1-x-2 x^3)/(-1+3 x^2+2 x^4),{x,0,40}],x]  (* _Harvey P. Dale_, Feb 18 2011 *)
%t A007455 LinearRecurrence[{0,3,0,2},{1,1,3,5},40] (* _Harvey P. Dale_, Feb 10 2015 *)
%o A007455 (Haskell)
%o A007455 a007455_list = 1 : 1 : 3 : 5 : zipWith (+)
%o A007455    (map (* 2) a007455_list) (map (* 3) $ drop 2 a007455_list)
%o A007455 a007455 n = a007455_list !! n
%o A007455 -- _Reinhard Zumkeller_, Jul 16 2012
%o A007455 (PARI) A007455(n)=[n%2*2+3,1]*([3,1;2,0]^(n\2-1))[,1] \\ _M. F. Hasler_, Jun 19 2019
%Y A007455 Cf. A007481, A007482, A007484.
%K A007455 nonn,easy,nice
%O A007455 0,3
%A A007455 _N. J. A. Sloane_, _Mira Bernstein_