%I A099425
%S A099425 1,2,6,14,34,82,198,478,1154,2786,6726,16238,39202,94642,228486,551614,
%T A099425 1331714,3215042,7761798,18738638,45239074,109216786,263672646,
%U A099425 636562078,1536796802,3710155682,8957108166,21624372014,52205852194
%N A099425 Expansion of (1+x^2)/(1-2*x-x^2).
%C A099425 Binomial transform of A094024(n+1).
%C A099425 a(n) is the number of matchings of the corona C'(n) of the cycle graph 
               C(n) and the complete graph K(1); in other words, C'(n) is the graph 
               constructed from C(n) to which for each vertex v a new vertex v' 
               and the edge vv' is added. Example: a(3)=14 because in the graph 
               with vertex set {A,B,C,a,b,c} and edge set {AB,AC,BC,Aa,Bb,Cc} we 
               have the following 14 matchings: the empty set, the six singletons 
               containing one of the edges, {Aa,BC},{Bb,AC},{Cc,AB},{Aa,Bb},{Aa,
               Cc}, {Bb,Cc} and {Aa,Bb,Cc}. Row sums of A102413. - Emeric Deutsch 
               (deutsch(AT)duke.poly.edu), Jan 07 2005
%C A099425 Apart from first term, same as A002203. - Peter Shor, May 12 2005.
%F A099425 a(n)=(1+sqrt(2))^n+(1-sqrt(2))^n-0^n; a(n)=a(n)=sum{k=0..n, A000129(n+1-k)C(1, 
               k/2)(1+(-1)^k)/2}. a(n)=2*A001333(n)-0^n.
%Y A099425 Cf. A102413.
%Y A099425 Sequence in context: A070933 A059570 A018016 this_sequence A105635 A025257 
               A110152
%Y A099425 Adjacent sequences: A099422 A099423 A099424 this_sequence A099426 A099427 
               A099428
%K A099425 easy,nonn
%O A099425 0,2
%A A099425 Paul Barry (pbarry(AT)wit.ie), Oct 15 2004