

A103425


a(n)=3a(n1)+a(n2)3a(n3).


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
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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 primefree? The general linear thirdorder recurrence equation x(n) = a*x(n1) + b*x(n2) + c*x(n3) 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.: (15x^2)/((1x^2)(13x)); 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



