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.

1, 1, 2, 2, 4, 10, 22, 52, 130, 326, 832, 2162, 5674, 15032, 40178, 108154, 292956, 797994, 2184430, 6006028, 16579138, 45929838, 127656504, 355863330, 994735442, 2787537904, 7829586914, 22038759218, 62158281844, 175636481738, 497142172806, 1409444977380

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Programs

PARI

a(n)=polcoeff((x+x^2-sqrt(1-2*x-x^2-6*x^3+x^4+x*O(x^n)))/2,n)

Formula

G.f.: (1 + x + x^2 - sqrt(1 - 2*x - x^2 - 6*x^3 + x^4))/2. - Michael Somos, Jun 08 2000

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