A025247 a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ... + a(n-3)*a(3) for n >= 4, with initial terms 2, 0, 1, 2.

2, 0, 1, 2, 4, 9, 22, 56, 146, 388, 1048, 2869, 7942, 22192, 62510, 177308, 506008, 1451866, 4185788, 12119696, 35227748, 102753800, 300672368, 882373261, 2596389190, 7658677856, 22642421206, 67081765932, 199128719896, 592179010350, 1764044315540

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Paul Barry, Jacobsthal Decompositions of Pascal's Triangle, Ternary Trees, and Alternating Sign Matrices, Journal of Integer Sequences, 19, 2016, #16.3.5.

Programs

Mathematica

Rest[CoefficientList[Series[(1+2x-Sqrt[1-4x+4x^2-4x^3])/2, {x,0,40}], x]]  (* Harvey P. Dale, Apr 23 2011 *)

PARI

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

Formula

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

Conjecture: n*a(n) +2*(3-2*n)*a(n-1) +4*(n-3)*a(n-2) +2*(9-2*n)*a(n-3)=0. - R. J. Mathar, Aug 14 2012