A090041 a(n) = 10*a(n-1) - 20*a(n-2), a(0)=1, a(1)=6.

1, 6, 40, 280, 2000, 14400, 104000, 752000, 5440000, 39360000, 284800000, 2060800000, 14912000000, 107904000000, 780800000000, 5649920000000, 40883200000000, 295833600000000, 2140672000000000, 15490048000000000

Offset: 0

Author

Paul Barry, Nov 20 2003

Keywords

• easy
• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (10,-20).

Crossrefs

Cf. A090139, A117317.

Formula

G.f.: (1-4*x)/(1-10*x+20*x^2) = (1-4*x)/((1-(5-sqrt(5))*x)*(1-(5+sqrt(5))*x)).

E.g.f.: exp(5*x)*(cosh(sqrt(5)*x) + sinh(sqrt(5)*x)/sqrt(5));

a(n) = ((1+sqrt(5))*(5+sqrt(5))^n - (1-sqrt(5))*(5-sqrt(5))^n)/(2*sqrt(5)).

Fifth binomial transform of (1, 1, 5, 5, 25, 25, ...). - Paul Barry, Nov 22 2003

3rd binomial transform of Fibonacci(3n+1). - Paul Barry, Mar 23 2004

a(n) = Sum_{k=0..n} A117317(n,k)*4^k. - Philippe Deléham, Jan 28 2012