%I A116406
%S A116406 1,1,2,3,7,11,26,42,99,163,382,638,1486,2510,5812,9908,22819,39203,
%T A116406 89846,155382,354522,616666,1401292,2449868,5546382,9740686,21977516,
%U A116406 38754732,87167164,154276028,345994216,614429672,1374282019,2448023843
%N A116406 Expansion of ((1+x-2x^2)+(1+x)sqrt(1-4x^2))/(2(1-4x^2)).
%C A116406 Interleaving of A114121 and A032443. Row sums of A116405. Binomial transform 
               is A116409.
%C A116406 Appears to be the number of n-digit binary numbers not having more zeros 
               than ones; equivalently, the number of unrestricted Dyck paths of 
               length n not going below the axis. - R. Stephan (ralf(AT)ark.in-berlin.de), 
               Mar 25 2008
%F A116406 a(n)=A114121(n/2)*(1+(-1)^n)/2+A032443((n-1)/2)*(1-(-1)^n)/2.
%F A116406 a(n)=sum{k=0..floor(n/2), binomial(n-1,k)}; - Paul Barry (pbarry(AT)wit.ie), 
               Oct 06 2007
%Y A116406 Sequence in context: A121268 A101173 A005246 this_sequence A112843 A036651 
               A049454
%Y A116406 Adjacent sequences: A116403 A116404 A116405 this_sequence A116407 A116408 
               A116409
%K A116406 easy,nonn
%O A116406 0,3
%A A116406 Paul Barry (pbarry(AT)wit.ie), Feb 13 2006