A025244 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

LINKS

Table of n, a(n) for n=1..32.

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

PROG

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

CROSSREFS

Sequence in context: A308986 A100088 A217212 * A132824 A298898 A339830

Adjacent sequences: A025241 A025242 A025243 * A025245 A025246 A025247

KEYWORD

nonn,changed

AUTHOR

Clark Kimberling

STATUS

approved

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