A025248 - OEIS

%I #10 Jun 15 2022 10:26:15

%S 1,0,2,2,2,6,14,26,58,142,326,754,1826,4438,10750,26378,65354,162334,

%T 405046,1016546,2561074,6472550,16415086,41761786,106526810,272411054,

%U 698275622,1793763282,4617047618,11906277750,30757124830,79582907370,206231537770

%N a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-3)*a(3) for n >= 4.

%F G.f.: (1+x-sqrt(1-2*x+x^2-8*x^3))/2. - _Michael Somos_, Jun 08 2000

%F Conjecture: n*a(n) +(-2*n+3)*a(n-1) +(n-3)*a(n-2) +4*(-2*n+9)*a(n-3)=0. - _R. J. Mathar_, Feb 25 2015

%o (PARI) a(n)=polcoeff((x-sqrt(1-2*x+x^2-8*x^3+x*O(x^n)))/2,n)

%K nonn

%O 1,3

%A _Clark Kimberling_