A025254 a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ... + a(n-3)*a(3) for n >= 4, with initial terms 3, 1, 1, 3.

3, 1, 1, 3, 10, 34, 118, 417, 1497, 5448, 20063, 74649, 280252, 1060439, 4040413, 15488981, 59701236, 231236830, 899559100, 3513314664, 13770811198, 54152480421, 213585706927, 844723104691, 3349274471386, 13310603555085, 53012829376985

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Crossrefs

Cf. A178578.

Programs

Mathematica

CoefficientList[Series[(1+3*x+x^2-Sqrt[x^4+2*x^3+7*x^2-6*x+1])/(2*x),{x,0,20}],x] (* Vaclav Kotesovec, Mar 02 2014 *)

Formula

G.f.: (1 + 3*x + x^2 - sqrt(x^4 + 2*x^3 + 7*x^2 - 6*x + 1))/(2*x). - Vaclav Kotesovec, Mar 02 2014

Recurrence: (n+1)*a(n) = 3*(2*n-1)*a(n-1) - 7*(n-2)*a(n-2) - (2*n-7)*a(n-3) - (n-5)*a(n-4). - Vaclav Kotesovec, Mar 02 2014