%I A097075
%S A097075 1,0,2,3,9,20,50,119,289,696,1682,4059,9801,23660,57122,137903,332929,
%T A097075 803760,1940450,4684659,11309769,27304196,65918162,159140519,384199201,
%U A097075 927538920,2239277042,5406093003,13051463049,31509019100,76069501250
%N A097075 Expansion of (1-x-x^2)/(1-x-3x^2-x^3).
%C A097075 Counts closed walks of length n at a vertex of a triangle, to which a 
               loop has been added at one of the other vertices.
%F A097075 a(n)=(1+sqrt(2))^n/4+(1-sqrt(2))^n/4+(-1)^n/2; a(n)=a(n)+3a(n-2)+a(n-3); 
               a(n)=(-1)^n/2+sum{k=0..floor(n/2), binomial(n, 2k)2^k}/2; a(n)=(-1)^n/
               2+A001333(n)/2.
%Y A097075 Cf. A000129, A051927, A097076.
%Y A097075 Sequence in context: A106519 A006866 A121908 this_sequence A036673 A111189 
               A001004
%Y A097075 Adjacent sequences: A097072 A097073 A097074 this_sequence A097076 A097077 
               A097078
%K A097075 easy,nonn
%O A097075 0,3
%A A097075 Paul Barry (pbarry(AT)wit.ie), Jul 22 2004