A152594 a(n) = -5*a(n-1)-2*a(n-2), n>1 ; a(0)=1, a(1)=-1 .

1, -1, 3, -13, 59, -269, 1227, -5597, 25531, -116461, 531243, -2423293, 11053979, -50423309, 230008587, -1049196317, 4785964411, -21831429421, 99585218283, -454263232573, 2072145726299, -9452202166349, 43116719379147

Offset: 0

Author

Philippe Deléham, Dec 09 2008

Keywords

• sign
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (-5,-2).

Crossrefs

Cf. A052984, A147703.

Programs

Mathematica

LinearRecurrence[{-5,-2},{1,-1},30] (* Harvey P. Dale, Jun 18 2015 *)

Formula

G.f.: (1+4*x)/(1+5*x+2*x^2).

a(n) = Sum_{k=0..n-1} A147703(n,k)*(-2)^(n-k).

a(n) = (-1)^n*A052984(n-1), n>=1 ; a(0)=1.

E.g.f.: exp(-5*x/2)*(17*cosh(sqrt(17)*x/2) + 3*sqrt(17)*sinh(sqrt(17)*x/2))/17. - Stefano Spezia, Jun 17 2025