cp's OEIS Frontend

A025244 a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ... + a(n-3)*a(3) for n >= 4, with initial terms 1, 1, 2, 2.

%I A025244 #15 Jan 16 2025 11:18:37
%S A025244 1,1,2,2,4,10,22,52,130,326,832,2162,5674,15032,40178,108154,292956,
%T A025244 797994,2184430,6006028,16579138,45929838,127656504,355863330,
%U A025244 994735442,2787537904,7829586914,22038759218,62158281844,175636481738,497142172806,1409444977380
%N A025244 a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ... + a(n-3)*a(3) for n >= 4, with initial terms 1, 1, 2, 2.
%F A025244 G.f.: (1 + x + x^2 - sqrt(1 - 2*x - x^2 - 6*x^3 + x^4))/2. - _Michael Somos_, Jun 08 2000
%F A025244 Conjecture: n*a(n) +(-2*n+3)*a(n-1) +(-n+3)*a(n-2) +3*(-2*n+9)*a(n-3) +(n-6)*a(n-4)=0. - _R. J. Mathar_, Feb 25 2015
%o A025244 (PARI) a(n)=polcoeff((x+x^2-sqrt(1-2*x-x^2-6*x^3+x^4+x*O(x^n)))/2,n)
%K A025244 nonn
%O A025244 1,3
%A A025244 _Clark Kimberling_