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A103425 a(n)=3a(n-1)+a(n-2)-3a(n-3). 1
1, 3, 5, 15, 41, 123, 365, 1095, 3281, 9843, 29525, 88575, 265721, 797163, 2391485, 7174455, 21523361, 64570083, 193710245, 581130735, 1743392201, 5230176603, 15690529805, 47071589415, 141214768241, 423644304723, 1270932914165 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..26.

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

Sequence in context: A145939 A161703 A018551 * A119472 A018568 A038375

Adjacent sequences:  A103422 A103423 A103424 * A103426 A103427 A103428

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Feb 05 2005

STATUS

approved

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Last modified January 21 08:09 EST 2020. Contains 331104 sequences. (Running on oeis4.)