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A025247 a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-3)*a(3) for n >= 4. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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.

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

MATHEMATICA

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

PROG

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

CROSSREFS

Sequence in context: A071496 A071502 A074704 * A127767 A292577 A055509

Adjacent sequences:  A025244 A025245 A025246 * A025248 A025249 A025250

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified July 13 13:48 EDT 2020. Contains 335688 sequences. (Running on oeis4.)