%I A007679 M3359
%S A007679 1,1,4,9,16,31,64,129,256,511,1024,2049,4096,8191,16384,
%T A007679 32769,65536,131071,262144,524289,1048576,2097151,4194304,
%U A007679 8388609,16777216,33554431,67108864,134217729,268435456,536870911
%N A007679 If n mod 4 = 0 then 2^(n-1)+1 elif n mod 4 = 2 then 2^(n-1)-1 else 2^(n-1).
%D A007679 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A007679 M. E. Larsen, Summa Summarum, A. K. Peters, Wellesley, MA, 2007; see 
               p. 37. [From N. J. A. Sloane (njas(AT)research.att.com), Jan 29 2009]
%D A007679 I. Nemes et al., How to do Monthly problems with your computer, Amer. 
               Math. Monthly, 104 (1997), 505-519.
%F A007679 2^(n-1) + cos(n*Pi/2).
%F A007679 Sum 2^k*C(n-k, 2k)*n/(n-k), k = 0..[ n/3 ].
%F A007679 a(n) = A007909(n) + A007910(n).
%p A007679 f:=n->2^(n-1)+cos(Pi*n/2);
%Y A007679 Sequence in context: A073141 A093175 A138992 this_sequence A068037 A167188 
               A014764
%Y A007679 Adjacent sequences: A007676 A007677 A007678 this_sequence A007680 A007681 
               A007682
%K A007679 easy,nonn
%O A007679 1,3
%A A007679 N. J. A. Sloane (njas(AT)research.att.com), R. K. Guy, Simon Plouffe.