%I #12 Jun 15 2022 10:48:24
%S 1,1,3,7,13,29,71,163,377,913,2219,5375,13189,32677,81167,202523,
%T 508273,1280537,3236275,8207543,20880893,53263405,136205527,349137811,
%U 896881641,2308523809,5953138875,15378562415,39791453685,103115768885,267597960095
%N a(n) = (1/2)*s(n+3), where s = A025248.
%F G.f.: (1-x-4*x^3-sqrt(1-2*x+x^2-8*x^3))/(4*x^3). - _Michael Somos_, Jun 08 2000
%F Conjecture: +(n+3)*a(n) +(-2*n-3)*a(n-1) +n*a(n-2) +4*(-2*n+3)*a(n-3)=0. - _R. J. Mathar_, Feb 25 2015
%o (PARI) a(n)=polcoeff((-sqrt(1-2*x+x^2-8*x^3+x^4*O(x^n)))/4,n+3)
%Y Cf. A025248.
%K nonn
%O 1,3
%A _Clark Kimberling_