OFFSET
0,2
COMMENTS
Binomial transform of A103424.
This is a (3, 1, -3) weighted tribonacci sequence, cf. A102001. The current sequence contains primes, including 3, 5, 41, 21523361. Is there an (a, b, c) weighted tribonacci sequence with a, b, c relatively prime which is prime-free? The general linear third-order recurrence equation x(n) = a*x(n-1) + b*x(n-2) + c*x(n-3) has a solution in terms of roots of a cubic polynomial, see Weisstein. - Jonathan Vos Post, Feb 05 2005
LINKS
Eric Weisstein's World of Mathematics, Linear Recurrence Equation.
Index entries for linear recurrences with constant coefficients, signature (3,1,-3).
FORMULA
G.f.: (1-5x^2)/((1-x^2)(1-3x)).
E.g.f.: exp(x)(1+sinh(2x)).
a(n) = 1 + (3^n - (-1)^n)/2.
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Feb 05 2005
STATUS
approved